Republican presidential nominee Donald Trump has accused rival Hillary Clinton of being "pumped up" during their last debate, saying they should both be tested for drugs before the next one.

He also suggested the presidential race was looking like a "rigged election".

The comments came in the wake of a string of sex assault claims against him and the publication of a recording in which he made obscene remarks.

Polls suggest Mr Trump is losing ground in some of the key battleground states.

Speaking at a rally in New Hampshire, Mr Trump said Mrs Clinton had been "all pumped up" at the beginning of the last debate but could "barely reach her car" at the end.

"We should take a drugs test," he said.

He did not provide any evidence to back up his claim.

Increasing personal attacks - Laura Bicker, BBC News, Washington

He's nicknamed her Crooked Hillary, said he would put her in prison if he was elected president, described her as not having the stamina for the job and now he has accused her of taking some kind of drug.

His rally speeches have become increasingly agitated and he has stepped up his rhetoric aimed at casting doubt on the fairness of this election, saying it is being rigged by a corrupt media pushing false allegations and outright lies.

Meanwhile the Clinton campaign has hit back against Mr Trump's contention that women accusing him of sexual assault are part of a scheme to help elect Mrs Clinton president.

Voting was to be encouraged and not "dismissed or undermined because a candidate is afraid he's going to lose", Clinton campaign manager Robby Mook said.

Mr Mook said he expected a record turnout because voters could see through what he described as Mr Trump's "shameful attempts to undermine an election weeks before it happens".

Republican House of Representatives Speaker Paul Ryan said he was "fully confident" that the November election would be carried out "with integrity", according to his spokeswoman AshLee Strong.

Mr Ryan, the most senior elected US Republican official, has said he will not defend Donald Trump in the wake of the recording of the nominee's obscene comments.

However, Mr Ryan has stopped short of ending his endorsement of the Republican candidate.

The latest sex assault accusations include those made by an ex-Apprentice contestant who cited a 2007 incident and a woman who described a case from the early 1990s.

Mr Trump denies attacking them.

"Nothing ever happened with any of these women. Totally made up nonsense to steal the election. Nobody has more respect for women than me!" he tweeted.

The final televised debate takes place on Wednesday.