Facing the prospect that they may never be able to impeach President Biden, House Republicans are exploring a pivot to a different strategy: issuing criminal referrals against him and those close to him.

In recent weeks, a political and factual reality has set in on Capitol Hill. Despite their subpoenas and depositions, House Republicans have been unable to produce any solid evidence of wrongdoing by Mr. Biden and lack the votes in their own party to charge him with high crimes and misdemeanors, the constitutional standard for impeachment.

Instead, top G.O.P. lawmakers have begun strategizing about making criminal referrals against Mr. Biden, members of his family and his associates, essentially sending letters to the Justice Department urging prosecutors to investigate specific crimes they believe may have been committed.

The move would be largely symbolic, but it would allow Republicans in Congress to save face while ending their so far struggling impeachment inquiry. It has the added appeal for the G.O.P. of aligning with former President Donald J. Trump’s vow to prosecute Mr. Biden if he wins the election.

And it would avoid a repeat of the humiliating process House Republicans, who have a tiny and dwindling majority, went through last month with the impeachment of Alejandro N. Mayorkas, the homeland security secretary. After initially falling short of the votes to impeach Mr. Mayorkas, Republicans barely succeeded on the second try, only to realize that the Democratic-controlled Senate was poised to quickly acquit him — or even dismiss the charges without a trial.

“There’s nothing that I’ve heard in the last couple of weeks that says that we are anywhere close to having the votes” for impeachment, said Representative Kelly Armstrong, Republican of North Dakota and the author of the resolution authorizing the impeachment investigation.

Mr. Armstrong said he believed criminal referrals were the much more likely outcome. Mr. Armstrong suggested House Republicans could make referrals regarding alleged violations of the Foreign Agents Registration Act in connection with international business deals by Hunter Biden, the president’s son, and suggested that the Justice Department investigate accusations of obstruction.

“I’m still interested in why we haven’t gotten better answers on the whole-of-government approach to obstructing all of these investigations,” Mr. Armstrong said.

Republicans say they are not finished with their investigation, and could still change course and decide to hold an impeachment vote. They have scheduled a public hearing next week with former business partners of Hunter Biden, though Mr. Biden himself has refused to appear.

In an interview, Representative Jim Jordan, Republican of Ohio and the Judiciary Committee chairman, said he was also demanding audio recordings of President Biden that were part of the special-counsel investigation by Robert K. Hur into his handling of classified documents.

Criminal referrals, Mr. Jordan said, were among the options “on the table” as the House G.O.P. moves forward.

Representative James R. Comer, Republican of Kentucky and chairman of the Oversight Committee, has repeatedly suggested in recent weeks that issuing criminal referrals could mark the end of the impeachment inquiry, rather than an impeachment vote.

“At the end of the day, what does accountability look like? It looks like criminal referrals. It looks like referring people to the Department of Justice,” Mr. Comer said in a recent interview with Fox News’s Sean Hannity. “If Merrick Garland’s Department of Justice won’t take any potential criminal referrals seriously, then maybe the next president, with a new attorney general, will.”

The shift to exploring criminal referrals came after Mr. Comer had what his aides say was a chance meeting last month with Mr. Trump in Florida. A spokeswoman for Mr. Comer would not comment on what was discussed, but said that while having lunch with Vernon Hill, a banker who has donated to Mr. Trump’s campaigns, the chairman unexpectedly ran into Mr. Trump and they had a brief 10-minute conversation.

The potential change in strategy also comes as Republicans have lost seats in the House, making impeachment all the more unlikely. With the departure next week of Representative Ken Buck, Republican of Colorado, the party will be down to 218 votes in the House, a bare majority of the 435-member body.

On Thursday, Speaker Mike Johnson confirmed that Republican leaders were discussing the possibility of criminal referrals.

In a brief interview at the Capitol, he made clear that impeaching President Biden was not his top priority at the moment, saying he’d been “a little busy with appropriations.” But he said House leadership would consider whether to issue criminal referrals.

“There’s more deliberation to be done on it — that’s for sure,” he said.

 

Representative Matt Gaetz, Republican of Florida and a close ally of President Trump, has been among those arguing for House Republicans to issue criminal referrals against Mr. Biden and his family members.

“He deserves them,” Mr. Gaetz said of Mr. Biden.

Mr. Gaetz added that it was clear that Republicans did not have the votes for impeachment.

“I don’t think that a sufficient number of Republicans hold the view I do that a bribe can be consummated through a payment to a family member,” said Mr. Gaetz, who has alleged that Hunter Biden’s income from overseas companies was little more than a bribery scheme. But he added that should Mr. Trump win election, he could install new personnel atop the Justice Department who could pursue prosecutions based on the Republicans’ referrals.

“The D.O.J. is about to change hands,” Mr. Gaetz said. “It’s about to be under new management.”

Criminal referrals would be a politically easier move for House Republicans than impeachment. They do not require a vote of Congress or even carry any legal weight. Mr. Comer could simply draft a letter laying out the allegations.

The Democratic-run special House committee that investigated the Jan. 6, 2021, attack on the Capitol made major headlines in the last Congress with its criminal referrals of Mr. Trump. (He was later charged by the Justice Department with crimes related to the plan to overturn the 2020 election.)

Delegate Stacey Plaskett of the Virgin Islands, the top Democrat on the Judiciary panel on the weaponization of government, said Republicans were merely trying to salvage a flailing investigation. Republicans took a brutal blow when one of the key pieces of evidence they touted was discredited by the Justice Department.

“They realize that they don’t have the votes for an impeachment because they don’t have the evidence,” said Ms. Plaskett. “But they recognize that by a criminal referral, it’s going to take some time, if there’s a referral, for it to work through the Justice Department, which gives them additional fodder during the election cycle. They’re just trying to create some kind of false equivalency between Donald Trump and Joe Biden, which is not there.”

Even some Republicans said a referral against Mr. Biden might not make sense, citing the Justice Department’s policy against prosecuting a sitting president.

“We don’t refer a seated president for criminal charges,” said Representative Darrell Issa, Republican of California. He added that Republicans can refer the president’s family members based on evidence they’ve discovered, “but most of what we’ve discovered they already knew.”

Representative Clay Higgins, Republican of Louisiana, who as a member of the Oversight Committee participated in the closed-door deposition of Hunter Biden, said he believed the investigation had “clearly” crossed the threshold of reasonable suspicion of the Biden family but had not yet established “probable cause” that the president had committed a crime.

“If our investigation reveals that impeachment is not a righteous pursuit, perhaps a criminal referral is,” Mr. Higgins said.

But Mr. Higgins also suggested House Republicans could simply let the voters decide.

“It’s a much heavier lift for impeachment. So I would say that no matter what the Oversight Committee does, the American people are going to have an opportunity in November to make a decision.”