Democrat Joe Biden told a raging President Donald Trump to "shut up" in a chaotic opening debate that turned almost immediately into a shouting match weeks ahead of the most tense US election in recent memory.

The debate in Cleveland, Ohio, was as bad-tempered as had been feared, with Trump leading the way in yelling over his challenger and the Fox News moderator Chris Wallace alike.

There was no handshake as the two men took the stage and while this was due to COVID-19 restrictions, the absence of the traditional greeting symbolized divisions through the country in the final countdown to November 3.

Trump went as hard on 77-year-old Biden as he'd threatened, saying the "radical left" had the centrist Democrat "wrapped around their little finger".

And he got personal, seeking to rile the former vice president by accusing one of his sons of corruption, and telling Biden that "there's nothing smart" about him.

Biden, though, not only gave as good as he got — he launched the kind of attack on Trump the billionaire president has rarely had to endure to his face.

"Liar," "racist" and "clown" were just some of the missiles launched from Biden, who also branded Trump the "puppy" of Russian President Vladimir Putin.

At times, neither Biden nor Wallace could get a word in, as Trump loudly touted his economic record and went after Biden's son Hunter.

"This will go down as one of the worst debates in history," Aaron Kall, a presidential debate specialist at the University of Michigan, told AFP.

 Conspiracy theories 

At one point an exasperated Biden, who leads strongly in the polls, turned to Trump and said: "Will you shut up, man!"

That moment symbolised Biden's performance in an arena where Trump's campaign had for months been predicting he would crumble.

The Republican had spread lurid conspiracy theories right up until the last minute that Biden would need drugs or an earpiece secretly providing answers to get through the night.

The anger-filled event did nothing to calm fears around the country that the presidential election, taking place in the middle of an ongoing coronavirus pandemic, could end in chaos.

Asked by Wallace whether they pledged to urge calm and refrain from declaring victory if the results are not immediately known November 3, Biden said: "Yes”.

Trump, though, wouldn’t commit, saying that if he saw "tens of thousands of ballots being manipulated, I can’t go along with that”.

And when asked if he condemned far-right armed militias like the Proud Boys, Trump gave a cryptic reply: "Proud Boys — stand back and stand by.”

The paramilitary group later appeared to adopt the phrase, with a social media account linked to the Proud Boys posting a logo that read "Stand Back, Stand By.”

Direct to American people 

Biden sought to tie Trump squarely to the COVID-19 pandemic that has claimed more than 200,000 lives in the United States, more than in any other country.

And he came with a visible plan to dodge the Trump rhetorical storm by frequently turning to face the cameras directly and addressing the tens of millions of people watching across the country.

"How many of you got up this morning and had an empty chair at the kitchen table because someone died of COVID?” Biden said, channeling his famed ability to show empathy for the suffering — something that Trump has long had difficulty in matching.

Mocking the 74-year-old Trump for one of his more notorious statements on supposed cures for coronavirus, Biden said: "Maybe you could inject bleach in your arm and that would take care of it.”

Tax avoidance 

Before they even appeared for the first of their scheduled three 90-minute TV debates, Biden was capitalising on bombshell revelations in The New York Times that the businessman managed to avoid paying almost any federal income taxes for years.

Trump — who has broken longtime presidential transparency by refusing to publish his tax returns — reportedly used loopholes to pay just $750 in federal tax during the first year of his presidency.

Hours before the Cleveland showdown, Biden published his own tax returns — and at the debate demanded that Trump do likewise.

Trump insisted at the debate that he has paid "millions” in taxes.

But the affair continues to provide Biden ammunition to try and chip away at Trump’s crucial support from blue collar voters or what the Republican calls "the forgotten men and women”.