Democrat Hillary Clinton has accused Republican Donald Trump of having a long history of racist behaviour during a heated presidential debate that could reshape the 2016 campaign for the White House.

Key points: Both candidates accuse each other of falsehoods

Both candidates accuse each other of falsehoods Mr Trump defends his tax record, saying it shows he is smart

Mr Trump defends his tax record, saying it shows he is smart Mrs Clinton says at least she has a plan for defeating IS

Mrs Clinton and Mr Trump interrupted each other throughout the debate on topics ranging from foreign policy to the economy.

Mr Trump said Mrs Clinton had very little to show for her many years in public life.

Mrs Clinton, a former secretary of state, and Mr Trump, a real estate tycoon, slammed each other for the controversy stoked for years by Mr Trump over whether President Barack Obama was born in the United States.

The President, who was born in Hawaii, released a long-form birth certificate in 2011 to put the issue to rest. Only this month did Mr Trump say publicly that he believed President Obama was US-born.

"He [Trump] has really started his political activity based on this racist lie that our first black president was not an American citizen," Mrs Clinton said

"There was absolutely no evidence for it. But he persisted. He persisted year after year."

Mr Trump repeated his false accusation that Mrs Clinton's failed 2008 presidential campaign against President Obama had initiated the so-called 'birther' issue.

"Nobody was pressing it, nobody was caring much about it … I was the one that got him to produce the birth certificate and I think I did a good job," Mr Trump said.

African-American voters overwhelmingly support Mrs Clinton, but Mr Trump in recent weeks has said he believes his policy agenda would benefit them and said the policies of President Obama and Mrs Clinton had failed to help black Americans.

He said Mrs Clinton's arguments were disingenuous.

"When you try to act holier than thou, it really doesn't work," Mr Trump said.

Charges of falsehoods fly back and forth

Sorry, this video has expired The first presidential debate of the 2016 US election campaign saw both candidates interrupting each other over a range of topics

Each accused the other of distortions and falsehoods and urged viewers to check their campaign websites for the facts.

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Mrs Clinton called the New York businessman's tax policies "Trumped-up trickle-down" economics and Mr Trump accused the former secretary of state of being "all talk, no action".

"I have a feeling I'm going to be blamed for everything," said Mrs Clinton, the first woman to win the presidential nomination of a major US political party, during one tough exchange.

"Why not?" retorted Mr Trump, a real estate tycoon and former reality TV star making his first run at public office.

Mrs Clinton knocked Mr Trump for not releasing his income tax returns and said that decision raised questions about whether he was as rich and charitable as he has said.

She noted that the few years of tax returns he had released showed that despite his wealth, he had paid no federal income tax.

"That makes me smart," Mr Trump said.

"I have a tremendous income," he said at one point, adding that it was about time that someone running the country knew something about money.

Mrs Clinton criticised Mr Trump for failing to pay some of the business people with whom his company had contracted. She said she had met a lot of people who had been cheated by her opponent.

Mr Trump said such incidents of non-payment had taken place when the work was unsatisfactory.

Polls show Mrs Clinton and Mr Trump are the least-liked candidates in modern history. ( Reuters: Joe Raedle )

Mr Trump attacked Mrs Clinton for her trade policies and said she would approve a controversial trade deal with Asian countries despite opposing it as a candidate.

"You were totally in favour of it, then you heard what I was saying, how bad it is, and you said, 'Well, I can't win that debate,' but you know that if you did win, you would approve that," he said.

Mrs Clinton rejected the criticism.

"Well Donald, I know you live in your own reality, but that is not the facts," she said.

Moderator Lester Holt struggled to rein in the candidates, with discussions about trade policy suddenly shifting to the fight against Islamic State as Mr Trump accused Mrs Clinton of giving away information to the enemy by revealing on her website how she planned to defeat the group.

Mrs Clinton said that unlike Mr Trump, she at least had a plan for fighting Islamist militants.

Opinion polls show tight race

Opinion polls have shown the two candidates in a very tight race, with the latest Reuters/Ipsos polling showing Mrs Clinton ahead by 4 percentage points, with 41 per cent of likely voters.

A second Reuters/Ipsos poll released on Tuesday (AEST) showed half of America's likely voters would rely on the debates to help them make their choice.

More than half, 61 per cent, were hoping for a civil debate and were not interested in the bitterness shown on the campaign trail.

The size of the television-viewing audience was expected to challenge the record of 80 million Americans who watched 1980's encounter between Democratic president Jimmy Carter and Republican Ronald Reagan.

Professor of government at Harvard University and president of the American Political Science Association, Jennifer Hochschild, told 7.30 there was a chance Mr Trump could win the election.

"He could win. We have said over and over, I and every other pundit or academic I can think of, 'This guy's a joke, he's not going to make it past February, past May, past June, past July', and of course here he is," she said.

"So I think all the political science models we've relied on, that I teach, don't work very well in this election."

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 10 minutes 11 seconds 10 m 'Donald Trump could win' ( Hayden Cooper )

Professor Hochschild said Mr Trump's negative approach struck a chord with voters.

"There is a segment of the American population ... who have largely been left out over the last 20 or 30 years," she said.

"It's a nationalist, relatively localist, relatively underemployed, people who feel as though the world is passing them by, who feel there's too many of the wrong kind of people coming into my country, too many gays, too many this and that.

"They feel like religion is being denigrated, and that's a population who I think, rightfully, are very angry and he's done a brilliant job of bringing them to the surface — and now we have to deal with it."

Clinton, Trump 'least-liked candidates in modern history'

Both Mr Trump and Mrs Clinton, shown in opinion polls to be the least liked White House candidates in modern history, hoped to use the debate to erase lingering voter doubts and address campaign-trail weaknesses.

The stakes are enormous. Mrs Clinton once had a sizable lead, but that has evaporated amid more questions about her family's foundation and use of a private email server while secretary of state under President Obama.

If the election were held today, Mrs Clinton would still defeat Trump, with an 88 per cent chance of reaching the 270 electoral college votes needed, according to the Reuters/Ipsos States of the Nation project, which is based on a weekly online tracking poll of more than 15,000 Americans.

Two other presidential candidates — Libertarian Gary Johnson and Green Party candidate Jill Stein — were not invited to take part in the debate because neither had obtained at least 15 per cent support in national polls, the threshold established to qualify.