The flags of 194 nations line the headquarters of the World Health Organisation in Geneva. They bear the colours of its "194 bosses" or member states. "And they all think we're too friendly with the others," sighs spokeswoman Dr Margaret Harris.

But it's two countries, in particular, now occupying the attention of the WHO as it grapples with its first major pandemic since it formed at the end of World War II.

China and the United States, both facing criticism for their handling of the COVID-19 crisis at home, are pointing the finger at one another. And, after praising China for its transparency, despite the country's initial attempts to keep the outbreak quiet, the WHO has come under fire itself. US President Donald Trump offered an early performance review of the United Nations agency in April when he tweeted, "The W.H.O. really blew it". Days later, he announced he was pulling the agency's US funding.

When the world first got a taste of what a new coronavirus could do, in the panic of the SARS outbreak 20 years ago, the WHO was applauded for how it swung into action, marshalling nations to stamp out the virus within months. This time the virus on the loose is even more dangerous, spreading faster and further than SARS, often undetected, yet deadlier than the flu, with no known treatments or vaccines.

Since SARS, the world is still more connected but a new mood of nationalism is testing diplomacy. Many experts warn the WHO is now facing the world's worst outbreak in a century in a weakened state – hamstrung by decades of funding cuts, bureaucracy and political pressure.

So what powers does the WHO actually have and why is it struggling to get countries to follow its advice?

What is the WHO?

On April 7 1948, 72 years ago to the day that Trump fired off that angry tweet, the WHO was born. As the first specialised arm of the newly formed UN, it had a sweeping mandate to lift people everywhere to the "highest standards" of health – and big plans to wipe out infectious diseases such as malaria. But even then countries didn't want it getting involved in their sovereign affairs. The organisation was given responsibility but no enforcement power, says global health expert at the University of Sydney Adam Kamradt-Scott. When its malaria eradication program failed, so too did its plans to take a "hands on" approach, he says. During the Cold War, it instead proved its value as a health diplomat – encouraging its own arms race between the US and the Soviets in smallpox vaccinations under a program that eventually saw the disease wiped off the face of the Earth by 1981.

Today, with more than 150 offices around the world but a budget roughly the size of some hospitals, the WHO is still largely a coordinating body, organising vaccination programs, convening research groups, tracking drug resistance and helping countries improve their healthcare. As Liberal MP Dave Sharma writes: "If we didn't have [the WHO], we'd have to invent it."

When an outbreak hits, it's the agency tasked with leading the world's response, juggling science, politics and logistics. It can declare a public health emergency of international concern (or a PHEIC, which is rather unfortunately pronounced "fake"), distribute resources, make recommendations to countries and demand scientific justification if they're ignored or exceeded. The agency can also call on its members to report outbreaks within their borders if it hears word of them. But if they refuse, Harris admits the WHO's only real option is to "name and shame" – and even that can cause headaches.

"There's no [precedent] of fining or throwing anyone out," she says. "We're a science organisation, we don't have any police powers."

Countries join the WHO by ratifying the UN treaty that underpins it. Funding comes from their membership dues and now mostly via voluntary contributions from nations and private donors tied to specific projects, with very little in the tank for emergencies.

Like all UN bodies, the WHO has been accused of bending to the will of the superpowers China and America. But Kamradt-Scott says almost one-third of its member states are from the African bloc and these nations hold a lot of sway too. It was from African politics that the current director-general Tedros Adhanom Ghebreyesus emerged, although, when his election secured backing from Beijing, he was also widely considered "China's pick".

Sometimes the WHO has been condemned for doing too little, such as when it waited so long to declare an emergency during the 2014 Ebola outbreak in Africa that the UN had to step in. At other times, it's been accused of crying wolf, hurting economies by pushing for tough containment measures against disasters that never arrived. When it became clear that the world's last pandemic, swine flu in 2009, was not as deadly as first thought, the WHO was accused of amplifying the crisis to benefit the pharmaceutical companies some of its experts worked with. The agency was cleared of any undue influence or wrongdoing by three separate reviews but Kamradt-Scott notes it never fully embraced the call for transparency that followed.

Harris admits the WHO pulled too far back after swine flu ("and I do wonder if that flu is why we struggle to convince countries to prepare for pandemics [we know] are coming"). But while the "chronically underfunded" agency still relies largely on goodwill and experts volunteering their time, she says it has now ramped up its role on the ground to fill gaps that emerged during the Ebola crisis.

"We're now right out there, under gunfire, where it's too dangerous for [charities and] other services to go," she says. Already, a WHO staffer has been lost in the COVID-19 fight – a driver ferrying samples of the virus out of Myanmar was shot dead in April.

How did the WHO respond to COVID-19?

Back at WHO HQ in Geneva, a small team of disease hunters was listening "to the chatter" online when the first signs of the outbreak appeared on social media and medical forums. By then, Harris says, it was already the last day of 2019, about a month or two after scientists suspect the virus first jumped from wild animals into humans.

"We usually see something earlier than that," she says. "But we saw some things online [on social media] first and then Wuhan's health services posted about these cases of atypical pneumonia they were getting so we went to China to find out more."

While countries are obligated to report to the WHO, the agency must wait for a formal invitation before sending in a team. "We can't just turn up on the doorstep and say, ‘We're the WHO, open up, show us all your labs'," Harris laughs. "No country is comfortable about the idea we've come to assess them. During [South] Korea's MERS outbreak [in 2015], it took them two weeks to let us in."

But Harris denied reports China had knocked back the WHO's initial requests to send in investigators, saying the agency's China office was already working on the ground in early January and Adhanom flew over later that month for a sit-down with China's President, Xi Jinping.

"It did take us a while ... about 10 days to set up who was going to be on the team [because] we try to get not just a range of experts but a range of different countries represented," Harris says.

WHO investigators did not test samples from the suspected source of the outbreak – a wet market in Wuhan known to sell wildlife – she says. Their focus was on the clinical data and the country's response as the outbreak took hold.

During this pandemic, as well as bringing together the best medical minds, the WHO is moving critical supplies around the world – including via an emergency UN air bridge due to travel bans – and helping coordinate drug and vaccine trails. If a vaccine proves successful, Harris says the agency will also help arrange an equitable and sensible rollout among nations.

Was the WHO too slow to act?

The agency's committee first met to assess the threat from the coronavirus in late January but, split down the middle, did not declare an emergency or PHEIC until a second meeting days later on January 30. Kamradt-Scott says the WHO has grown increasingly literal in its interpretation of an outbreak's risks – waiting for clear international spread rather than just the "potential" for it referred to in the guidelines. "Of course, by then the genie's out of the bottle."

Still, while the WHO did sound its top alert that day, the world was waiting for it to use another word: pandemic. Australia "declared" a pandemic on February 27. By the time the WHO used the term on March 11, the crisis had well exceeded its own definition, with cases in more than 100 countries. Making such a declaration no longer triggers any formal response, as it did under the old pandemic alert system ("That was quietly dismantled after swine flu," Harris says). But it would help guide country responses on the ground.

The agency had been calling for countries to move fast and aggressively from early on in the outbreak but some countries, including the US and the UK, dragged their heels and contributions to the WHO's COVID-19 emergency fund have been slow to trickle in. Harris says staff were nervous that declaring a pandemic – the top of the scale under the old system – would cause some governments to throw up their hands in defeat. "They'd stop testing, stop contact tracing and let it go, but what we were saying was, 'This one's different, you can stop it [using those] methods, Wuhan showed us that.'" But many saw the delay as deference to China.

Did the WHO favour China?

Questions have also been raised about why the WHO at times parroted advice from Beijing without confirming it. Most conspicuously, in early January it repeated China's assurances there was no evidence the virus could spread between people, despite reports in December of family and healthcare workers falling ill around patients. Some say this early confusion, as well as emerging evidence Chinese authorities initially covered up the outbreak, cost the world critical weeks in the COVID-19 fight. More than one study has found that if China had moved on containment even a week earlier, infections could have been cut by two thirds, and a case of COVID-19 has been retrospectively diagnosed in France as far back as December.

But when China did move, it was big. On January 23, it locked down the city of Wuhan, and later much of the country, in a containment strategy that raised human rights concerns even as it appeared to almost stamp out the virus by April. At the time, Adhanom said China was setting "the new standard for outbreak response". Harris says it was the country's aggressive testing and case detection that the WHO was praising, not necessarily the lockdown.

Returning from China in February, the WHO also stressed that they trusted its data – although months later it would be found to have been incomplete. Those additional cases were due to retrospective testing, the WHO says, but Harris notes it's "always a struggle" to get countries to share their data. Still, those early numbers, based off the first 55,000 cases in China, formed much of the world's understanding of the new virus – and assertions by the WHO that it did not appear to spread easily through people without symptoms also failed to stand the test of time.

The Chinese government's track record on outbreaks should have made the agency more suspicious from the start, Kamradt-Scott says. SARS was on the loose and kept secret for months before a WHO doctor raised the alarm as cases started to escape its borders. Even once WHO officials were allowed into China, they were made to wait days for permission to travel to the epicentre of the outbreak – and patients were even quietly moved out of sight into ambulances and hotels as the agency toured hospitals.

Is the WHO too weak?

Harris says that, unlike other organisations, the WHO's member state governance structure means it can only go so far in criticising or ordering around nations – and this time Adhanom "has gone as far as he can ... [he's been] a lot more aggressive than previous director-generals".

One notable exception is the woman who ran the WHO during SARS – the former prime minister of Norway, Dr Gro Harlem Brundtland. Brundtland was an ex-doctor – someone, like Adhanom, who had not yet been "WHO-ified", says Kamradt-Scott, but who was brought in to reform.

"After that doctor died ... who blew the whistle SARS had spread, she called China out publicly, and China let her in," Kamradt-Scott says. "She knew some of the world leaders personally, she just rang them on the phone, she didn't bother with the rules."

But when SARS disappeared, the economic cost of the WHO's measures, including directives against travel, was huge. Countries agreed it was time to find the "middle ground", Harris says, by reforming the International Health Regulations that govern how the WHO can respond to outbreaks. Kamradt-Scott sat in on those closed-door meetings. At first, it was about helping the WHO do what it did to stop SARS, he says. But China's embarrassment had a chilling effect too, and the agency was further muzzled even as it was granted more power to assess country pandemic preparedness and watch for outbreaks. "Some of the other Western countries thought, what if it's us next time?"

Is Australia's inquiry looking at the WHO?

Ahead of the World Health Assembly's now virtual meeting on May 18, Australia has been pushing for a global probe into the COVID-19 outbreak, including its handling by the WHO, and has floated the idea of granting the agency the same power to enter a country as weapons inspectors. At the WHO, Harris says, "we welcome the debate".

After weeks of secretive negotiations and despite significant resistance from China, Australia has now secured the support of the European Union's top foreign minister for an independent inquiry into the coronavirus. The EU will put forward a wide-ranging motion to the assembly to help unify the world's COVID-19 response, including a newly amended call for an inquiry run independent of the WHO itself. "We welcome the fact that many countries have joined the discussion," a spokesman for the Morrison government said days ahead of the assembly. "It is through open consultation and dialogue that [we] will learn lessons from this pandemic and position ourselves better to respond to future outbreaks."

Kamradt-Scott notes inspection powers have been proposed, and voted down, before - an easier fix would be to train WHO committees to better interpret the international laws that govern what they can already do.

Australia has also been calling on China directly to open up about the origins of the virus. While Australian, British and German intelligence agencies have shot down claims by Trump that the virus likely escaped from a lab in Wuhan, Prime Minister Scott Morrison wants a global ban on wildlife wet markets – where, as with SARS, it's believed the virus jumped from animals into humans. Scientists had long been warning the wildlife trade would give rise to another outbreak and, while the WHO has also advised against wet markets selling live wildlife for meat and parts, it's stopped short of condemning China's decision to leave them open after SARS and now COVID-19. Beijing has blasted Australia for its stance, calling it a US "lapdog" and threatening consumer boycotts.

Harris says Australia's push for a review is a step in the right direction, typical of its usual role as a "neutral honest broker" in global health, but reviews usually happen after an outbreak has tapered off. "Of course we have to have a review. After Ebola in 2014 we had six and we really changed a lot."

Still, when Ebola returned to Africa four years later, the WHO waited almost a year to declare another emergency.

In an interview with a Hong Kong broadcaster in March, the WHO's Bruce Aylward pretended not to hear a question about Taiwan's membership future and response to COVID-19 and then shut down the interview.

What does this mean for global health security?

Last month, President Trump announced he would suspend US funding to the WHO pending a review into its handling of the coronavirus crisis, accusing it of helping China cover up the extent of the outbreak. The move was widely seen as a ploy to divert attention away from the Trump administration's own missteps in responding to COVID-19. But experts warn the impact of the cuts, in the middle of a pandemic, could be considerable, and many other nations have leapt to the WHO's defence.

Of all its member states, the US has long given the lion's share of money – about 16 per cent of the total WHO budget. Harris says many existing programs, such as those to combat polio and AIDS in the developing world, will now suffer under the cuts. "Work we do in places like Africa where you can save millions of lives," she explains. "[America] has been such a big player in global health, not just in funding but in expertise. We just hope this whole situation resolves itself."

The WHO denies it made any attempt to hide information about the virus. If it has been influenced by China, Kamradt-Scott expects the evidence will emerge in time under a review but, for now, he's giving Adhanom the benefit of the doubt.

"He can't do what Brundtland did," he says. "I think Tedros went too far in heaping praise on China and he's made some early errors but he's also under more restrictions. It was critical he get into China. He probably thought he'd catch more flies with honey."

Still, the WHO needs more than just another post-outbreak debriefing, it needs a "roots and branch" review, he says, including more focus on transparency. ("We can livestream the UN security council, why can't we see at least a transcript of these emergency committee meetings?") The agency, made up of "almost exclusively medical doctors", could also benefit from bringing people on board with other expertise, he says, such as in interpreting international law or understanding travel bans.

But Kamradt-Scott stresses that, for all the agency's bureaucracy, those doctors are still dedicated people passionate about improving health. "There's no question we need the WHO. Especially now we live in a world where these outbreaks are becoming more frequent."

With something between a laugh and a sigh in her voice, Harris describes the world's response to COVID-19 so far as "the Olympics of public health". "It's all countries really, rich or poor, they're all utterly suspicious of the others, wondering why some are going better, getting more gold medals than they are ... It's diverting far too much energy. We're all in this together."

With Anthony Galloway