United States Vice President Kamala Harris savaged Republican presidential candidate Donald Trump as "extreme" and the friend of dictators, while he branded her a "Marxist" in a bitter televised debate Tuesday that poured fuel on an already explosive US presidential election.

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 agonisingly 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 and resorting to the kinds of colourful invective and often meandering insults that he uses at his rallies.

Harris, 59, 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."

Here are takeaways from the debate:

Handshake

Heading into the debate, there was a question as to how Harris and Trump, who have never met, would greet each other.

Harris settled the issue, definitively. She walked over to Trump at his podium, extended her hand and introduced herself as "Kamala Harris."

It was a disarming way for Harris to approach a man who has spent weeks insulting her race and gender.

After that, the debate quickly settled into an expected groove. Harris swiftly painted herself as a forward-looking candidate. She predicted Trump at the debate would pull from the "same tired playbook."

"A bunch of lies, grievances and name calling," Harris said.

Economy

"I believe in the ambition, the aspirations, the dreams of the American people, and that is why I imagine and have actually a plan to build what I call an opportunity economy," said Harris.

"Look, we've had a terrible economy, because inflation, which is really known as a country buster," said Trump.

"People can't go out and buy cereal or bacon or eggs or anything else. The people of our country are absolutely dying with what they've done. They've destroyed the economy," said Trump.

Additionally, Trump said that his Democratic rival had no economic plans of her own, and had copied President Joe Biden's policies.

"She doesn't have a plan. She copied Biden's plan, and it’s like four sentences... four sentences that are just, 'Oh, we’ll try and lower taxes.' She doesn't have a plan," he said during the prime-time showdown on ABC.

Israel-Gaza conflict

"It must end immediately, and the way it will end is we need a ceasefire deal, and we need the hostages out," said Harris.

"She hates Israel. If she's president, I believe that Israel will not exist within two years from now," said Trump to which Harris responded: "That's absolutely not true. I have my entire career and life supported Israel and the Israeli people."

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

"(Hungarian Prime Minister) Viktor Orban said the most respected, most feared person is Donald Trump. We had no problems when Trump was president," said Trump.

"Wait a minute, I'm talking now, if you don't mind, please, does that sound familiar?" said Trump, appearing to refer to Harris' use of "I'm speaking" during the 2020 vice presidential debate against former Vice President Mike Pence.

Abortion

"I pledge to you, when Congress passes a bill to put back in place the protections of Roe v Wade as president of the United States, I will proudly sign it into law," said Harris.

"Now, I believe in the exceptions for rape, incest and life of the mother. ... Now states are voting on it. ... Each individual state is voting. It's the vote of the people. Now it's not tied up in the federal government," said Trump.

Immigration

"I'll tell you something, he's going to talk about immigration a lot tonight, even when it's not the subject that is being raised," said Harris.

"Our country is being lost, we're a failing nation," Trump said, referring to people crossing into the country illegally.

Assassination attempt

"I probably took a bullet to the head for the things they say about me," said Trump.

"As I said, you're gonna hear a bunch of lies, and that's not actually a surprising fact," said Harris.

"There she goes again. It's a lie," said Trump after Harris said he would sign a national abortion ban were he to win office.

Jan 6, 2021, Capitol attack

"I had nothing to do with that, other than they asked me to make a speech," said Trump, when asked if he regretted anything that day.

"I was at the Capitol. I was the vice president-elect. I was also a senator and on that day, the president of the United States incited a violent mob to attack our nation's capital, to desecrate our nation's capital," said Harris.

"They are not going to have higher prices," Trump said, defending his tariffs proposal.

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."

"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."

COVID-19

"But what Donald Trump did, let's talk about this, with COVID, is he actually thanked President Xi for what he did during COVID," said Harris.

Project 2025

"What you're going to hear tonight is a detailed and dangerous plan called Project 2025 that the former president intends on implementing if he were elected again," said Harris.

Battle of taunts

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

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."

'Calm, cool and collected'

The last presidential debate in June doomed Biden's reelection campaign, after he delivered a catastrophic performance against Trump. Harris took over as nominee amid Democratic fears that Biden was too old and infirm to defeat the scandal-plagued Republican.

Biden told reporters he would watch the debate from New York — where he traveled on Tuesday ahead of ceremonies marking the anniversary of the September 11, 2001 attacks.

"I spoke to the vice president. She seems calm, cool and collected. I think she's going to do great," Biden said.

Tim Smith, 39, a Harris supporter, stood outside the debate venue holding a sign similar to those used by the Trump campaign but bearing the word "Loser."

Smith said he was hoping "we'll get to hear a little bit of the policies they want to institute — and not so much the name calling or the attacks."

The Democrats brought along two former Trump administration officials who are now harsh critics, including the short-lived White House communications director Anthony Scaramucci.

California Governor Gavin Newsom, a prominent Harris supporter, called her "the next generation of leadership in this country."

"It's daylight, and darkness, chaos versus competency, right and wrong, liberalism and illiberalism," he said.

Trump the 'boxer'

Harris has earned a reputation in past debates and while serving as a senator for ice-cold put-downs and tough questions.

But Trump is the most brutal public speaker in US politics.

He also benefits from an incredible ability to survive any scandal — and his fervent base if anything enjoys his frequent gaffes, fabricated stories and promotion of conspiracy theories.

He has been convicted of falsifying business records to cover up an affair with an adult film star, found liable for sexual abuse, and faces trial on charges of trying to overturn the 2020 election that he lost to Biden.

But he may surprise by opting for a more restrained performance, as he did in June, allowing Biden to self-destruct.

"You can't prepare for President Trump," his spokesman Jason Miller said. "Imagine like a boxer trying to prepare for Floyd Mayweather, or Muhammad Ali."