New York: The fog of scandal enveloping US President Donald Trump has grown thicker, with prosecutors examining whether his inaugural committee raised illegal funds and speculation mounting that Trump could face criminal prosecution when he leaves office.

President Donald Trump waves as he walks with first lady Melania Trump during the inauguration parade on Pennsylvania Avenue in Washington. Credit:Evan Vucci

Revelations about the criminal inquiry into Trump's inauguration came just a day after the President's former lawyer Michael Cohen was sentenced to three years in prison for offences including organising hush-money payments to two women who claimed to have affairs with Trump.

The chief legal analyst on Fox News, which is Trump's favourite television network, said it was clear that Trump had committed a crime by directing Cohen to make the payments.

A New York judge found the payments contributed illegal campaign contributions and audio has been released of Trump and Cohen discussing the payments in 2016.