The Republican nominee also suggested the presidential race was looking like a “rigged election”.
The comments came in the wake of the publication of a recording in which Donald Trump made inappropriate remarks, which sparked a string of assault claims.
According to latest polls, Donald Trump is losing ground in some of the key battleground states.
Speaking at a rally in New Hampshire, Donald Trump said Hilalry 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,” the billionaire said.
Donald Trump did not provide any evidence to back up his claim.
Meanwhile the Clinton campaign has hit back against Donald Trump’s contention that women accusing him of assault are part of a scheme to help elect Hillary Clinton president.
Voting was to be encouraged and not “dismissed or undermined because a candidate is afraid he’s going to lose”, Hillary Clinton’s campaign manager Robby Mook said.
Robby Mook said he expected a record turnout because voters could see through what he described as Donald 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.
Paul Ryan, the most senior elected Republican official, has said he will not defend Donald Trump in the wake of the recording of the nominee’s obscene comments.
However, Paul Ryan has stopped short of ending his endorsement of Donald Trump.
The latest person to come forward is 63-year-old Cathy Heller, who told the Guardian that Donald Trump grabbed her and “went for the lips” during their first and only meeting 20 years ago, during a Mother’s Day event at his Mar-a-Lago estate in Palm Beach, Florida.
A spokesman for Donald Trump rejected the claim.
Donald Trump has denied attacking any of the women who have made allegations against him, saying the claims are part of a plot to damage his campaign.
The final presidential debate takes place on October 19.
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