Jack Dorsey’s US payments giant Square has accused Australia's major banks of engaging in anti-competitive conduct when it entered the local market and described parts of the financial services laws as "challenging to navigate".

Square, which is listed on the New York Stock Exchange with a market capitalisation of $US30 billion ($44 billion), ruffled the Australian banks' feathers when it arrived in 2015 with card readers that plug directly into smartphones or tablets, making it easier for small businesses to accept credit card payments with existing devices.