The indictment of a former F.B.I. informant on charges of making up claims that President Biden and his son sought bribes from a Ukrainian energy company is the latest blow to the effort by House Republicans to assemble a credible impeachment case against the president.

Republicans had hailed the informant, Alexander Smirnov, as “credible” and “most respected.” They asserted that he had 17 recordings to back up his story that Mr. Biden and his son Hunter had each accepted bribes of $5 million from Burisma, the Ukrainian firm that had paid Hunter Biden as much as $1 million a year for serving on its board.

But the tapes never materialized, and on Thursday, the Justice Department announced that it had charged Mr. Smirnov with making it all up.

That left Democrats calling for the immediate halt of the inquiry, and Republicans scrambling to find something else to use against the president.

“He is lying and it should be dropped and it’s just been an outrageous effort from the beginning,” Mr. Biden told reporters at the White House on Friday.

Representative Jamie Raskin of Maryland, the top Democrat on the House Oversight Committee, said the indictment exposed the evidence being cited by Republicans as false. “I hope it will be the final chapter of this ludicrous wild goose chase,” Mr. Raskin said.

The charges against Mr. Smirnov are unlikely to deter Republicans from marching forward with their investigation into the president. But they deeply undercut the foundation of the inquiry and give more weight to longstanding Democratic complaints that the impeachment drive is a purely political exercise intended to put Mr. Biden on the defensive as he seeks re-election.

Mr. Smirnov, 43, is accused of falsely telling the F.B.I. that Hunter Biden demanded the money to protect the company from an investigation by the country’s prosecutor general. But those claims were false, and Mr. Smirnov’s motivation for lying appeared to have been political, prosecutors wrote, citing anti-Biden messages he wrote during the 2020 campaign.

“They’re making an impeachment inquiry based on — it looks like now — criminal conduct,” said Kimberly Wehle, a law professor at the University of Baltimore. “It’s not like where there’s smoke, there’s fire. It’s like the smoke is actually a lie and a federal felony.”

The charges against Mr. Smirnov are not the first time the central thesis of the Republican case — that Mr. Biden accepted bribes from Ukraine — has been undercut or shot down. Attempts to prove that Mr. Biden was on the take have repeatedly failed over the years, according to congressional testimony.

One example stemmed from an incident in 2019, as allies of President Donald J. Trump were hunting for allegations of corruption against Mr. Biden. Lev Parnas, an associate of Rudolph W. Giuliani, Mr. Trump’s personal lawyer at the time, secured an interview with the owner of Burisma, Mykola Zlochevsky, that the men hoped would prove a bribery allegation central to their case.

But the interview backfired, undercutting the claims of bribery. Mr. Giuliani became enraged and demanded that Mr. Parnas tell no one of what the Ukrainian had said, according to Mr. Parnas’s account to Congress.

“Make sure nobody sees this,” Mr. Giuliani said. “Bury this.”

Mr. Parnas concluded in a letter to Congress: “There was no evidence of bribery or extortion that anyone could find.”

Other officials who have undercut the Republican case against Mr. Biden include Petro Poroshenko, the former Ukrainian president; Kurt Volker, the Trump administration’s special representative for Ukraine negotiations; Gordon Sondland, Mr. Trump’s ambassador to the European Union; career U.S. State Department officials; and several of Hunter Biden’s business associates.

“To be clear, President Biden — while in office or as a private citizen — was never involved in any of the business activities we pursued,” testified Rob Walker, one of Hunter Biden’s business partners.

Upon taking over the House at the start of last year, Republicans vowed to carry out the investigation of Mr. Biden that Mr. Trump had long sought, in effect continuing the scrutiny of the involvement of the Bidens in Ukraine that had led to Mr. Trump’s first impeachment.

With newly acquired subpoena power and wide discretion allowing them to investigate nearly anything, House Republicans pursued bank records, suspicious activity reports and demanded interviews with the president’s family and associates.

The volumes of evidence they received have produced some favorable news cycles for Republicans. They found evidence backing up reports that Mr. Biden, as vice president, met and talked with some of his son’s business associates — and that he incorrectly asserted that Hunter Biden had never made any money from his deals in China — but they have failed to show that Mr. Biden was financially involved in any of his son’s business ventures, or that he changed U.S. policy to benefit his son’s associates.

Republicans claim to have found three instances in which family members sent money to Joseph R. Biden Jr. — while he was out of office — but they have often omitted the context that the exchanges were loan repayments, not a cut of income.

The House Oversight Committee has also released documents that showed that one of Hunter Biden’s businesses, Owasco PC, made three payments of $1,380 to his father in 2018. But other documents indicate the money was to pay back his father for helping to cover the cost of a Ford truck.

House Republicans have pointed to two payments — one for $200,000 and another for $40,000 — that James Biden, the president’s brother, made to him while he was out of office. They have characterized the $40,000 check as “laundered China money.” But they did not note evidence showing Joe Biden had first lent the money to his brother before being repaid.

Still, hard evidence is not needed for the House to march on with an impeachment inquiry, said Stanley Brand, a former top lawyer for the House.

“Based on what I’ve observed about the impeachment process over the last decade or two, it’s not strictly legally based,” Mr. Brand said. “The strict rules of evidence don’t apply. The standard Department of Justice policies and practices in a criminal case don’t apply. It’s not even clear from the text of the Constitution that an impeachable offense has to be a crime.”

Republicans have not limited themselves to merely looking at Hunter Biden’s work in Ukraine. They are also examining the way the Justice Department is run under President Biden, and whether he mishandled classified documents.

After the charges against Mr. Smirnov, Representative James R. Comer, the Kentucky Republican who is chairman of the Oversight Committee, issued a defiant statement in which he dismissed the idea that his investigation was flailing.

In a statement, he said the Republican case is “not reliant” on Mr. Smirnov, and pointed to testimony he said backed up his case against the Bidens.

“We will continue to follow the facts to propose legislation to reform federal ethics laws and to determine whether articles of impeachment are warranted,” Mr. Comer said.

It was also clear that Republicans were looking to pivot their inquiry to look more deeply into Mr. Biden’s handling of classified documents after a report from the special counsel Robert K. Hur raised questions about the president’s memory — and, they argued, fitness for office.

Republicans announced that they would delve deeper into that angle, starting with a demand for documents and testimony from the ghostwriter of Mr. Biden’s book, and public testimony from Mr. Hur.