Donald Trump demanded an investigation Monday after revelations that Hillary Clinton’s allies invested heavily in the state Senate campaign of a Democrat at a time when her husband oversaw part of the FBI’s investigation into Mrs. Clinton’s secret email account.

Mr. Trump said the revelations about now-FBI Deputy Director Andrew McCabe and his wife, Jill McCabe, a Democrat whose campaign collected hundreds of thousands of dollars from organizations overseen by Virginia Gov. Terry McAuliffe, are the latest example of corruption that pervades the nation’s capital.

“Hillary knew this money was being paid, and she has to be held accountable for this,” Mr. Trump said at a campaign rally in Florida.” She has to be held accountable because she knew that money, $675,000-plus, was being paid. So how is she allowed to continue to run for president?”

Down in the polls with two weeks to go before Election Day, Mr. Trump is struggling to recapture the attention of voters who have tuned him out over the past month.

He has delved more deeply into policy, laid out an agenda for his first days in office and increased his attacks on Mrs. Clinton and the “rigged” system he says is thwarting his campaign.

The McCabe revelations, first reported by The Wall Street Journal, gave him a new hook.

Mr. McAuliffe is a close friend, financier and political ally of the Clintons, and his 2013 governor’s campaign was seen as a test run for Mrs. Clinton’s own presidential bid.

His political action committee ponied up $467,500 to Mrs. McCabe’s campaign, and the state Democratic Party gave more than $200,000 at a time when Mr. McCabe headed the FBI’s Washington field office.

That field office provided the manpower for the investigation into Mrs. Clinton’s secret email system. Mr. McCabe would later be promoted to the third-ranking post at the FBI, and then named deputy.

Mrs. McCabe was running to unseat state Sen. Dick Black, a Republican, and ousting him would have swung control of the Virginia state Senate to Democrats.

Mr. Black, who won the race, said Mr. McCabe should resign from his post.

He also told The Washington Times that Mr. McAuliffe irked local Democrats last year by handpicking Mrs. McCabe to run for the seat. The senator said he wondered whether the money influenced the FBI’s investigation.

“It is kind of hard to imagine that a huge contribution of that magnitude to his wife would not consciously or subconsciously influence how he would decide the case,” Mr. Black said.

“Now I can’t say for certain, but this is the reason that the ethical standards say you should avoid even the appearance of impropriety because ordinary people looking at the facts would say this really stinks and this really, really smells of government corruption,” he said.

Brian Coy, a spokesman for Mr. McAuliffe, dismissed the idea that the governor engaged in questionable dealings, saying Mrs. McCabe was a “highly qualified candidate” and other candidates were the recipients of bigger donations.

“He had one face-to-face meeting with [Mr. McCabe], which occurred on March 7, 2015, before her decision to run,” Mr. Coy said in an email. “As the story itself states, Mr. McCabe was not in any position to influence the FBI investigation until AFTER the campaign concluded.

“The Governor had positively no connection to the email issue, he supported Dr. McCabe solely because she shared his vision for Virginia and any insinuation otherwise is ridiculous at best, reckless at worst,” he said.

The governor’s PAC, Common Good VA, gave 13 percent of its contributions to her campaign. Two other state Senate candidates received more money from the PAC, as did the state Democratic Party.

Mrs. Clinton’s campaign sent a memo accusing Mr. Trump of spinning conspiracy theories to keep his campaign afloat.

The Democratic presidential nominee campaigned in New Hampshire and, increasingly confident of victory, turned her attention to down-ticket races, appearing with Gov. Maggie Hassan, who is challenging Republican Sen. Kelly Ayotte.

Also appearing on the stage was Sen. Elizabeth Warren of Massachusetts, who attacked Mr. Trump over the lewd remarks he made about women in a 2005 video recording and adopted his description of Mrs. Clinton as a campaign mantra.

“Nasty women have really had it with guys like you. Yeah, get this, Donald: Nasty women are tough. Nasty women are smart. And nasty women vote,” she said. “And on Nov. 8, we nasty women are going to march our nasty feet to cast our nasty votes to get you out of our lives forever.”

Mrs. Clinton leads in New Hampshire by 8 percentage points and Florida by almost 4 percentage points, according to the Real Clear Politics average of polls. Nationally, her lead is five points.

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