House Republicans said on Monday that they would move this week to hold the F.B.I. director, Christopher A. Wray, in contempt of Congress, escalating their attacks on the federal law enforcement agency as they grasp for evidence of wrongdoing by President Biden.

Representative James R. Comer, the Kentucky Republican who is chairman of the Oversight Committee, made the announcement after summoning F.B.I. officials to Capitol Hill for a closed-door briefing on a document containing an unverified allegation of bribery against Mr. Biden when he was vice president. The Trump Justice Department investigated the allegation, which involved his son Hunter Biden’s dealings in Ukraine, in 2020, but prosecutors could not substantiate the claims, according to two people familiar with the matter.

Yet Mr. Comer, who has said he is investigating whether Mr. Biden traded on his office for money, has repeatedly insinuated that there is more to it; on Monday, he asserted that the allegation “has never been disproven.”

At the chairman’s insistence, Mr. Wray’s team brought the document to a secure area of the Capitol on Monday and briefed Mr. Comer and Representative Jamie Raskin of Maryland, the committee’s top Democrat, on it for about 90 minutes. But Mr. Comer complained afterward that the agency, citing concern about protecting the identity of the informant, declined to allow other members of the committee to view it.

“We will now initiate contempt of Congress hearings this Thursday,” Mr. Comer told reporters on Capitol Hill, adding, “The ball is in the F.B.I.’s court.”

The surfacing of the unsubstantiated allegation against Mr. Biden is the latest bid by Republicans to undermine the credibility of the F.B.I., which they have sought to vilify after the bureau and the Justice Department began investigations into President Donald J. Trump’s role in trying to overturn the 2020 election and his handling of classified documents after leaving the White House.

Republicans have relied on former F.B.I. agents — some of whom have embraced Jan. 6 conspiracy theories and have even accepted money from a Trump ally — to provide information against the bureau.

Mr. Raskin said the document Mr. Comer sought, and Mr. Wray provided, contained an allegation from an informant relaying a conversation with someone else, which the informant could not corroborate. He said the Justice Department under former Attorney General William P. Barr “found no reason to escalate it from an assessment to a so-called preliminary investigation.”

“What we’re talking about is secondhand hearsay,” Mr. Raskin said, adding, “That confidential human source said that he had no way of knowing about the underlying veracity of the things that he was being told.”

Calling attention to the document is Mr. Comer’s latest effort to keep public attention on Hunter Biden’s business activities, which Republicans have made a focus of their investigations for years.

“We are not interested in whether the allegations against Vice President Biden are accurate or not,” Senator Charles E. Grassley, Republican of Iowa, said last week on Fox News. “We’re responsible for making sure the F.B.I. does its job.”

Republicans have long alleged that Hunter Biden used his seat on the board of the Ukrainian energy company Burisma — for which he was paid substantial sums — to influence his father. A career State Department official even raised concerns with a senior White House official in 2015 about the situation.

The attention on Hunter Biden from the right reached a high point in 2020, after Mr. Trump’s personal lawyer Rudolph W. Giuliani began circulating materials about the younger Mr. Biden, including photos and documents from a laptop he had abandoned at a Delaware repair shop.

One person familiar with the material who insisted on anonymity to discuss it said some of it was junk that was plainly not credible. The bribery allegation against Mr. Biden was never elevated to a preliminary investigation, according to people familiar with the inquiry, but Mr. Brady did forward some information from his work to other prosecutors.

Richard P. Donoghue, then a top official in the Trump Justice Department, agreed with Mr. Brady that the matter did not need to be investigated further, according to one of the people familiar with the matter.

Representative Dan Goldman, Democrat of New York and a member of the Oversight Committee who examined allegations against Mr. Biden and Burisma as part of a House impeachment team in 2019, said the Republican narrative had fallen flat because Mr. Biden sought to crack down on corruption in Ukraine, not enable it.

“The facts are actually directly contrary to any of the Republican allegations,” Mr. Goldman said.

After the briefing Monday, Mr. Comer claimed the informant’s allegation “is currently being used in an ongoing investigation,” but Mr. Raskin described Mr. Comer as “recycling stale and debunked Burisma conspiracy theories long peddled by Rudy Giuliani.”

The F.B.I. went to some lengths to make the documents available to lawmakers, first inviting them to bureau headquarters and then bringing the material to the Capitol to accommodate their schedules.

“The F.B.I. has continually demonstrated its commitment to accommodate the committee’s request, including by producing the document in a reading room at the U.S. Capitol,” the bureau said in a statement on Monday. “The escalation to a contempt vote under these circumstances is unwarranted.”