Qantas Airways and Virgin Australia will immediately begin implementing US President Donald Trump's ban on immigration from seven majority Muslim nations, a decision that applies to Australians with dual citizenship.

The two airlines will instruct staff to refuse access to US-bound flights to citizens of Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen. Because customers aren't required to disclose their citizenship when they book tickets, some passengers could be turned away at airport check-in counters as they try to fly.