WHITE PLAINS, United States (AFP) - Republican presidential nominee Mr Donald Trump and his Democratic rival, Mrs Hillary Clinton, on Monday (Oct 10) headed back to the campaign trail after a fiery presidential debate, with the billionaire businessman looking to bounce back after a weekend that crippled his White House bid.

With just over four weeks to go before American voters head to the ballot boxes to choose their next commander-in-chief, the candidates travelled to swing states - Mr Trump to Pennsylvania and Mrs Clinton to Michigan and Ohio - to court voters.

On Sunday (Oct 9), before tens of millions of television viewers and a live audience including former US president Mr Bill Clinton and three women who have accused him of abuse, Mr Trump threatened to jail his Democratic rival and lobbed incendiary allegations against her former president husband.

The 70-year-old real estate mogul, seeking to stem the bleeding in his campaign after scores of Republicans deserted him, apologised on Sunday for "locker room talk" in which he bragged about groping women.

But he stated baldly that "Bill Clinton was abusive to women."

"If you look at Bill Clinton, far worse," Mr Trump insisted. "Mine are words, his was action," he said.

Shattering the last vestiges of political decorum, Mr Trump threatened the former secretary of state - whom he accused of having "hate in her heart" - with imprisonment if he wins the presidency.

"If I win, I'm going to instruct the attorney general to get a special prosecutor to look into your situation because there's never been so many lies, so much deception," Mr Trump said.

The 68-year-old former first lady and US senator, who is vying to be America's first female president, pushed back by saying Mr Trump's lewd comments merely showed his true self.

"This is who Donald Trump is, and the question for us, the question our country must answer is that this is not who we are," she said.

When Mrs Clinton said that it was "awfully good" that someone with Mr Trump's temperament was "not in charge of the law of our country", he shot back: "Because you'd be in jail."

Two separate polls showed Mrs Clinton had prevailed in the second of three presidential debates.

A CNN/ORC survey of debate watchers put her up 57-34 per cent, while a YouGov snap poll put her margin of victory closer at 47-42 per cent.

"I think last night he showed his heart to the American people. He said he apologised to his family, apologised to the American people, that he was embarrassed by it," Mr Trump's running mate Mike Pence told CNN on Monday.

"And then he moved on to the real choice in this election, which is really not just a choice between two candidates - it's a choice between two futures," said Mr Pence, who had said over the weekend he himself was "offended" by Mr Trump's remarks.

Mr Trump faces a make-or-break moment after his crude boasts, which he made in 2005 and which became public in a video released on Friday, as streams of Republicans have retracted their support for his campaign.

With a campaign based on earning free television air time and little ground game, Mr Trump is dependent on the Republican Party machinery to get out the vote.

The party leadership had been deeply angered by Mr Trump's misogynistic remarks, and Mr Pence said they were indefensible, though he was back on his side by Sunday night.

In an extraordinary step aimed at reversing the tide of public opinion, Mr Trump had convened a press event just minutes before the debate that included several women who accuse Mr Bill Clinton of sexual harassment and rape - later invited to attend the debate.

Introduced by Mr Trump as "very courageous women", the speakers included Ms Paula Jones, a former government employee in Arkansas who sued Mr Clinton for sexual harassment, and Ms Juanita Broaddrick, also of Arkansas, who claims that Mr Clinton raped her in 1978.

But Mr Trump needs a dramatic boost if he is to claw back ground against Mrs Clinton, who has surged in the polls since their first debate on September 26.

Dr Larry Sabato, who heads the Centre for Politics at University of Virginia, tweeted that "Trump has done well enough to stop GOP bleeding".

But Dr Dante Scala, political science professor at the University of New Hampshire, said he doubts Mr Trump can recover.

"I didn't see enough this evening to turn things around," Dr Scala said.

"The news of the last 48 hours will continue to settle into voters' minds and I'm not sure this debate will be enough in itself to change the trajectory of the race."

Mr Trump's threat to jail Mrs Clinton over her use of a private e-mail server while serving as secretary of state sparked a firestorm of criticism, as critics painted him as a dictator in the making.

"In the USA we do not threaten to jail political opponents. @realDonaldTrump said he would. He is promising to abuse the power of the office," President Barack Obama's former attorney general, Mr Eric Holder, said in a tweet.

A number of fellow Republicans also tarred Mr Trump as undemocratic.

"Winning candidates don't threaten to put opponents in jail," said former George W. Bush White House spokesman, Mr Ari Fleischer.

In Sunday's debate in St Louis, Mrs Clinton largely refused to respond to Mr Trump's barrage of attacks, opting to adhere to advice from First Lady Michelle Obama: "When they go low, you go high."

"This is not an ordinary time and this is not an ordinary election," she said.

But, as in the first debate, she also laid a series of traps for Mr Trump, prodding him toward admitting he had not paid federal income tax in around two decades.

"Donald Trump's trying to change the dynamic. But I would argue he's just digging the hole deeper with these attacks," Mrs Clinton's campaign manage Robby Mook told CBS on Monday.