PORTSMOUTH, N.H. — Donald J. Trump brought his beleaguered presidential campaign to the rear of a car dealership here Saturday afternoon, lobbing bombastic attacks on his opponent and even challenging her to submit to a drug test before the next presidential debate.

“I don’t know what’s going on with her,’’ Trump, the Republican nominee, told a rowdy crowd of about 2,000 that often booed Democratic candidate Hillary Clinton when Trump mentioned her name at the rally.

Seeming to imply that Clinton was on drugs during their last debate, Trump said, “At the beginning of her last debate, she was all pumped up. And at the end… she could barely reach her car.’’

Trump sought to reignite his embattled campaign by steering his remarks away from the fresh wave of sexual assault allegations woman have made against him and back onto tried-and-true themes such as his plans to build a wall on the US-Mexico border.

In New Hampshire, a key swing state where Trump has returned repeatedly, he also focused on the opioid epidemic that has taken a toll on communities across the Granite State and the country.

However, he soon veered from talk of a plan to cure opioid addiction to a claim that Clinton was “all pumped up’’ on drugs herself, suggesting that she take a drug test before they next debate.

“I’m willing to do it,’’ Trump said as the crowd laughed.

Clinton campaign officials didn’t respond directly to Trump’s insinuation that their candidate was taking drugs or his call for her to submit to a drug test. But in a statement that seemed to allude more to Trump’s claims the election will be rigged, Clinton campaign manager Robby Mook said “voters see through Donald Trump’s shameful attempts to undermine an election weeks before it happens.’’

Flanked by a “Make America Great Again’’ banner, Trump spoke Saturday for nearly 50 minutes here, sporadically touching on topics ranging from his disapproval of international trade deals to his plan to repeal the Affordable Care Act. Notably absent was a fervent defense against the wide-ranging accusations of sexual misconduct that have recently dogged the campaign.

Trump has previously denied the allegations and said, without evidence, that the women were acting in concert with a conspiracy against his candidacy. On Saturday, he briefly dismissed their allegations as “outright lies’’ and characterized some of his accusers as “crazy.’’

“We can’t let them get away with this, folks. Total lies.’’ Trump said of the accusations from multiple women. “We’re going to stop it. We’re not going to back down ... You have phony people coming up with phony accusations, with no witnesses whatsoever.’’

He made no mention of the recently unearthed video from 2005, which showed Trump bragging to "Access Hollywood’’ host Billy Bush about predatory behavior toward women.

Trump devoted the majority of his speech — when he wasn’t berating Clinton — to praising New Hampshire voters. In his third visit to the state in two weeks, Trump spoke fondly of how local voters helped catapult him atop the Republican Party against long odds and little support.

It was New Hampshire, back in February, that handed Trump his first state primary victory and cemented his transition from political outsider to presidential pacemaker. On Election Day, New Hampshire’s four electoral votes are destined to be hotly contested.

As of Saturday, the poll-tracking website Real Clear Politics found Clinton held a narrow 3.5 percent lead over Trump in New Hampshire.

“Donald Trump and New Hampshire fit each other,’’ said former New York City Mayor Rudy Giuliani, a top surrogate for Trump who spoke to the crowd Saturday. “He is his own man, and he’ll be your man! Your leader! Your champion!’’

In a reflection of the division in his party, New Hampshire’s Republican candidates for governor and the US Senate are split on whether or not they will vote for Trump in November. Incumbent US Senator Kelly Ayotte recently rescinded her support of Trump and said she will not vote for him in November. Chris Sununu, who is running for governor, has stuck with his endorsement of Trump but did not campaign with him Saturday.

Giuliani and US Senator Jeff Sessions of Alabama, another Trump adviser, revved the crowd before Trump’s arrival. They also laid the groundwork for the claims Trump later repeated: that the election was being rigged by a nebulous “they.’’

“Hillary Clinton is the most corrupt person ever to seek the office of the presidency,’’ Trump said. At another point, he asserted that Clinton was “plotting to destroy the [nation’s] sovereignty.’’

Trump repeated the claim of a rigged election at another rally Saturday, in Bangor, Maine. He also vowed to bring back manufacturing jobs, the Associated Press reported.

The crowd in Portsmouth, some clad in raunchy T-shirts and buttons that read “Hillary for Prison,’’ lauded their beloved candidate with the familiar chants of “President Trump’’ and “Lock her up’’ in reference to Clinton. Some parents screamed obscenities, with children on top of their shoulders.

At times, the crowd quieted as Trump read calmly from a teleprompter, promising to make addiction-curbing drugs more widely available and change laws to allow law enforcement officials to seize more fentanyl. But in an instant, as Trump returned to his popular themes of bashing Clinton, the media, and even fellow Republicans, the crowd perked up.

“USA! USA! USA!’’ supporters screamed as he promised that, if he is elected, “every dream you every dreamed for your family and your country’’ will come true. But, Trump warned, there will be dire consequences if he loses.

“If we don’t win ... our country will be in a spiral that won’t be stopped,’’ Trump said. “On Nov. 8, the arrogance on Washington D.C. will come face to face with the righteous verdict of the American voter.’’

The crowd roared in approval.

Herndon can be reached at astead.herndon@globe.com.