Washington | Kamala Harris repeatedly got under the skin of Donald Trump in their first presidential debate, challenging him on foreign policy, economy and abortion as she sought to erase the memory of President Joe Biden's disastrous face-off earlier with the Republican candidate.

“You're not running against Joe Biden. You're running against me,” Vice President Harris, who is the Democratic candidate, told the former president, when he criticised the current administration.

The matchup on TV Tuesday night began with a handshake – Harris took the initiative walking up to Trump's lectern – but later descended into acrimony.

“I think you've heard tonight two very different visions for our country, one that is focused on the future and the other that is focused on the past and an attempt to take us backwards. But we're not going back," Harris, 59, said in her remarks towards the end of the 90-minute debate in Pennsylvania.

She claimed the world leaders are “laughing at Donald Trump”, and pulled no punches. “I have talked with military leaders, some of whom worked with you, and they say you're a disgrace,” she said.

Trump, 78, asked why Harris had not done during the Biden-Harris administration what she is promising now.

“She just started by saying she's going to do this, she's going to do that. She's going to do all these wonderful things. Why hasn't she done it? She's been there for three and a half years,” he said.

“They've had three and a half years to fix the border. They've had three and a half years to create jobs and all the things we talked about. Why hasn't she done it?” he asked in his concluding remarks.

This was the second presidential debate but the first between Trump and Harris.

Biden put up a terrible performance against Trump in the first debate, and withdrew from the race, paving the way for Harris to be the Democratic Party's nominee for the November elections.

The debate moderators from ABC News had to inject fact-checks multiple times during the debate.

“As I said, you're going to hear a bunch of lies, and that's not actually a surprising fact,” Harris said.

She said if Trump is re-elected, he would sign a national abortion ban bill. "There would be a national abortion monitor that would be monitoring your pregnancies, your miscarriages," she claimed.

"I think the American people believe that certain freedoms, in particular, the freedom to make decisions about one's own body, should not be made by the government,” she said.

Trump countered that the abortion policy should be determined by the states.

There she goes again. It's a lie. I'm not signing a ban, and there's no reason to sign a ban because we've gotten what everybody wanted. Democrats, Republicans, and everybody else and every legal scholar wanted it to be brought back into the states, and the states are voting,” he said.

The two sparred over election rallies.

“It's a really interesting thing to watch. You will see, during the course of his rallies, he talks about fictional characters like Hannibal Lecter. He will talk about windmills cause cancer. And what you will also notice is that people start leaving his rallies early out of exhaustion and boredom,” she jibed.

And Trump accused Harris – without providing evidence -- of paying people to attend her campaign events.

"We have the biggest rallies, the most incredible rallies in the history of politics. That's because people want to take their country back. Our country is being lost," he said.

“I believe very strongly that the American people want a president who understands the importance of bringing us together and that we have so much more in common than what separates us. And I pledge to you to be a president for all Americans,” Harris said.

US commentators said Harris had done better in the debate.

Fox News, often considered partial towards Trump, said in its headline to an opinion piece, “In the Trump-Harris face-off there was a clear winner but don't believe this election is over.” On economy, the former president countered Harris. “Everybody knows what I'm going to do, cut taxes very substantially and create a great economy like I did before. We had the greatest economy. We got hit with a pandemic. We did a phenomenal job with the pandemic.” Trump called Harris a Marxist who is now adopting his philosophy.

“Everything that she believed three years ago and four years ago is out the window. She's going to my philosophy now... But if she ever got elected, she'd change it, and it will be the end of our country. She's a Marxist. Everybody knows she's a Marxist. Her father is a Marxist professor in economics, and he taught her well,” Trump said.

Trump claimed that Harris has been the Biden administration's “border czar” and blamed her for “these millions and millions of people that are pouring into our country monthly”.

Many of these people coming in are criminals, and that's bad for America's economy, he said.

"Well, bad immigration is the worst thing that can happen to our economy. They have and she has destroyed our country with a policy that's insane,” he alleged.

The moderators from ABC News had to inject fact-checks multiple times during the debate.

Harris said the US needs a leader who engages in solutions and addresses the problems at hand. “But what we have in the former president is someone who would prefer to run on a problem instead of fixing a problem,” she said.

Harris was seen interrupting Trump several times during the debate. It was not heard as the mikes of non-speakers were muted during the debate.

Trump vowed that he would end the war between Russia and Ukraine if he wins the election.

The former president, who raised Afghanistan several times during the debate, called the chaotic 2021 withdrawal of American troops "the most embarrassing moment in the history of the United States".

Harris said she agreed with Biden's commitment to get the US out of the country, and it was important to remember how the withdrawal came to be. “Donald Trump as president negotiated one of the weakest deals you can imagine," she charged, referencing his negotiations with the Taliban.

Trump claimed that Harris "hates Israel" while she fired back that he "admires dictators." He claimed Israel would be destroyed within two years if he lost the election and Harris assumed office as president.