Miami, Florida - Donald Trump unleashed a torrent of abuse against President Joe Biden on Tuesday, mercilessly assailing the embattled Democrat as he faces calls to end his re-election bid after a disastrous debate performance.

Trump's speech in Miami was his first public appearance since the clamor for Biden's withdrawal began gaining momentum, and the gloves were emphatically off as the Republican accused Democrats of lying to protect the president.

"It's the biggest cover up in political history," Trump thundered near the start of a 75-minute speech, which focused almost entirely on his 81-year-old election rival.

"As you know, they are all co-conspirators in the sinister plot to defraud the American public about the cognitive abilities of the man in the Oval Office."

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Commentators have noted how Trump has appeared relatively restrained in recent days, stepping back from the limelight to allow the full glare of the media to stay on the Democratic leadership crisis.

But he dispensed with any pretense at restraint as he characterized Biden as a "corrupt, incompetent, cognitively impaired" leader who was barely aware of his own policies or record in office.

In a typically bombastic speech peppered with multiple exaggerations and falsehoods, Trump accused Biden of going missing regularly from the Oval Office while his son Hunter, a convicted felon – like Trump himself – runs the government aided by first lady Jill Biden.

For much of the rally at his Doral National golf resort, Trump ran through his usual rambling stump speech, characterizing America as teetering on the edge of catastrophe and describing a world facing a race against the clock to avert nuclear Armageddon.

But there were multiple departures as Trump skewered Biden over the many public statements from elected Democrats in recent days questioning his ability to carry the party to victory in November.

The former president dared his successor to another debate without moderators and, in a lighter moment that raised a smile from audience members baking in 103-degree Fahrenheit heat, challenged him to a round of golf.

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"It will be among the most watched sporting events in history, maybe bigger than the Ryder Cup or even the Masters," he deadpanned.

"And I will even give Joe Biden 10 strokes a side... and if he wins, I will give the charity of his choice, any charity that he wants, $1 million. And I bet you he doesn't take the offer."

During one low point in the debate, the two rivals had sparred over who had a better long game, and the Biden campaign's response to the latest challenge came in the form of a golf pun.

"Joe Biden doesn't have time for Donald Trump's weird antics – he's busy leading America and defending the free world," it said.

"Donald Trump is a liar, a convict, and a fraud only out for himself par for the course."

Florida Senator Marco Rubio is a frontrunner in the contest to be named Trump's running mate at next week's Republican nominating convention in Milwaukee, and he was in the front row to cheer on Trump and deliver brief remarks of his own.

Nearby, a digital billboard underscored the evolution that the Republican Party has undergone under Trump, playing 2016 footage of Rubio eviscerating the man he is hoping to work with for the next four years.

"You all have friends that are thinking about voting for Donald Trump," the now staunchly loyal Rubio was seen telling a crowd in Texas. "Friends do not let friends vote for con artists."