Philadelphia, Pennsylvania - Kamala Harris savaged Donald Trump as "extreme" and the friend of dictators, while he branded her a "Marxist" in a bitter televised debate Tuesday that was filled with false claims by the Republican.

On hot-button issues ranging from abortion and race to the fate of US democracy, the two held their first – and possibly only – debate ahead of the November 5 election, with each hoping for a breakthrough in an agonizingly close race.

Trump, who only a few weeks ago had believed himself to be cruising to victory, reacted to pressure from Harris by raising his voice, losing his cool, and resorting to the kinds of insults and meandering rants that he uses at his rallies.

Harris responded by looking on in amusement, then clearly got under his skin, declaring that she represents a fresh start after the "mess" of the Trump presidency, and saying: "We're not going back."

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The ABC News debate began when the Democratic vice president unexpectedly approached the Republican former president to shake his hand, before they took to their lecterns in the National Constitution Center in Philadelphia.

Then the niceties ended.

Within minutes, 78-year-old Trump called her a "Marxist" and also falsely claimed that she and President Joe Biden had allowed "millions of people pouring into our country from prisons and jails, from mental institutions and insane asylums."

It was only of many lies, which included claims about babies being "aborted" after birth and an insistence that the long-exonerated Central Park Five were actually guilty of the murder of white female jogger in 1989.

Harris pointed out that Trump is a convicted felon, called him "extreme" and said it is "a tragedy" that throughout his career he had used "race to divide the American people."

One of their most jarring exchanges was on Trump's unprecedented refusal to accept losing to Biden in the 2020 election, before trying to overturn the result.

In front of the audience expected to run into the tens of millions of voters, Trump doubled down, insisting there is "so much proof" that he really won.

Harris turned to Trump and said that his own former security officials in the White House have called him a "disgrace."

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"World leaders are laughing at Donald Trump," she said.

Trump would "give up" Ukraine to Russian leader Vladimir Putin, "a dictator who would eat you for lunch," she charged. "Dictators and autocrats are rooting for you to be president again."

Another intense exchange was on abortion.

Trump insisted that while having pushed for the end of the federal right to abortion, he wanted individual states to make their own policy.

Harris said he was telling a "bunch of lies" and called his policies "insulting to the women of America."

Having already irritated Trump, she then needled him on one of his favorite topics: crowd sizes at rallies, where attendees were leaving early out of "exhaustion and boredom."

The angered 78-year-old's response veered wildly into a debunked racist conspiracy theory that Haitian immigrants have been eating local people's pets in Ohio.

"They're eating the dogs, the people that came in, they're eating the cats," he said before being corrected by the ABC moderator David Muir that the authorities in the town of Springfield have said this did not happen.

Having given a performance extremely light on policy – but still more substantial than Trump's – the sitting vice president was seen as a clear winner by two-thirds of viewers polled by CNN.