PORTSMOUTH, N.H. — Escalating his criticism of Hillary Clinton’s debate performances, Donald J. Trump came to a state battling a drug epidemic and suggested without any evidence on Saturday that his opponent had been on drugs during their second debate.

“I think we should take a drug test prior to the debate,” Mr. Trump told a crowd of thousands gathered in the parking lot of a Toyota dealership on a chilly afternoon.

He continued: “We should take a drug test prior because I don’t know what’s going on with her. But at the beginning of her last debate — she was all pumped up at the beginning, and at the end it was like, ‘Oh, take me down.’ She could barely reach her car.”

When asked for comment, the Clinton campaign directed reporters to a statement by Robby Mook, the campaign manager, that was put out earlier in the day in response to Mr. Trump’s allegations of a “rigged” election.