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.

Clinton and Trump interrupted each other throughout the debate on topics ranging from foreign policy to the economy. Trump said Clinton had very little to show for her many years in public life.

Clinton, a former secretary of state, and Trump, a real estate tycoon, slammed each other for the controversy stoked for years by 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 Trump say publicly that he believed 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. There was absolutely no evidence for it. But he persisted. He persisted year after year," Clinton said.

Trump repeated his false accusation that Clinton's failed 2008 presidential campaign against 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," Trump said.

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

He said Clinton's arguments were disingenuous.

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

Clinton, 68, wore a red pantsuit, and Trump, 70, wore a dark suit and a blue tie to the encounter that could shift the course of the tight race for the November 8 election. She called him Donald, and he called her Secretary Clinton.

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

Clinton called the New York businessman's tax policies "Trumped-up trickle-down" economics and 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 Clinton, the first woman to win the presidential nomination of a major US political party during one tough exchange.

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

Clinton knocked 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," 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.

Clinton criticised 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.

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

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

Clinton rejected the criticism.

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

A second Reuters/Ipsos poll released on Monday 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. Some commentators forecast Super Bowl-sized viewership of about 100 million people.