US presidential candidate Donald Trump, holding his first campaign rally since surviving an assassination attempt a week ago, rejected concerns he was a threat to America's democratic system, telling the crowd: "I took a bullet for democracy."

"I'm not an extremist at all," the newly-crowned Republican presidential nominee continued at the rally in swing state Michigan, dismissing his reported links to Project 2025, a manifesto from the Heritage Foundation that has been characterised by opponents as an authoritarian, right-wing wish list.

And he mocked the rival Democratic Party, roiled by unprecedented pressure for US President Joe Biden to abandon his re-election bid, amid concerns over his age and fitness to serve, if re-elected.

"They have no idea who their candidate is...this guy [Biden] goes and he gets the votes, and now they want to take it away. That's democracy," Trump told the 12,000-strong crowd of supporters.

In the fiery, but typically rambling speech, the Republican riffed on his hardline immigration views, espoused falsehoods about migrant crime, and repeated his baseless claim that Democrats "rigged" the 2020 election. (AFP)