The Republican-led House is on track to approve a formal impeachment inquiry into President Biden on Wednesday, pushing forward with a yearlong G.O.P. investigation that has failed to produce evidence of anything approaching high crimes or misdemeanors.

Republicans say the vote, which is expected in the evening, is needed to give them full authority to carry out their investigations amid anticipated legal challenges from the White House. Democrats have denounced the inquiry as a fishing expedition and a political stunt.

G.O.P. leaders refrained for months from calling a vote to open an impeachment inquiry, given the reservations of mainstream Republicans, many of them from politically competitive districts, about moving forward without proof that Mr. Biden had done anything wrong. But the political ground has shifted considerably, and most of them are now willing to do so, with some emphasizing that they are not yet ready to charge the president.

Representative Tom Cole, Republican of Oklahoma and chairman of the Rules Committee, portrayed the vote as a largely procedural step to shore up the House’s investigatory powers.

“Since September, the House has been engaged in an impeachment inquiry, examining whether sufficient grounds exist for the House to exercise constitutional power to impeach the president of the United States,” Mr. Cole said. “Today’s resolution simply formalizes that inquiry, and grants the House full authority to enforce its subpoenas that have been denied as recently as today.”

But Representative Jim McGovern, Democrat of Massachusetts, said there was nothing but rank politics at play.

“We are here for one reason and one reason alone: Donald Trump demanded that Republicans impeach, so they are going to impeach,” Mr. McGovern said. “They are weaponizing and abusing impeachment, one of the most somber and serious things that Congress can do, to attack President Joe Biden.”

The vote was scheduled to take place just hours after Hunter Biden, the president’s son and a main focus of the Republican investigation, defied a subpoena to sit for a private deposition. In a dramatic moment outside the Capitol on Wednesday morning, the younger Mr. Biden held a news conference in which he repeated his offer to publicly testify in the investigation into his father, but insisted again that he would not be interviewed behind closed doors. He has said he fears that Republicans would leak selectively from his testimony in efforts to distort it.

Republicans have issued a subpoena to the younger Biden, demanding to question him over his business dealings in Ukraine, China and other countries as they attempt to portray him as corrupt and link the deals to his father.

“I am here,” Mr. Biden said on Wednesday morning. “Let me state as clearly as I can: My father was not financially involved in my business — not as a practicing lawyer, not as a board member of Burisma, not my partnership with a Chinese private businessman, not in my investments at home nor abroad and certainly not as an artist.”

The Republicans leading the impeachment inquiry, including Representatives James R. Comer of Kentucky, the chairman of the Oversight Committee, and Representative Jim Jordan of Ohio, the chairman of the Judiciary Committee, threatened to hold him in contempt of Congress if he does not comply with demands for private testimony.

“We think he should come in and so if he doesn’t, we’re going to move forward with contempt proceedings,” Mr. Jordan said.

Since winning the majority, House Republicans have been investigating myriad aspects of President Biden’s family and administration, hunting for evidence that could be used to prove he is corrupt and should be impeached. Former President Donald J. Trump, still seething over being impeached twice, has urged on their investigation at every step.

The Republican inquiry has focused heavily on Hunter Biden, who is under indictment on federal tax and gun charges, and the work he did for companies and partners overseas. They are also examining whether the Biden administration interfered with the Justice Department investigation of Hunter Biden and whether President Biden mishandled classified documents when he was vice president or as a senator.

Using their subpoena power, Republicans have obtained more than 36,000 pages of bank records; 2,000 pages of suspicious activity reports from the Treasury Department; and dozens of hours of testimony from two of Hunter Biden’s business partners, a senior official from the National Archives and Records Administration, seven federal agents and three U.S. attorneys.

“President Biden must be held accountable for his lies, corruption and obstruction,” Mr. Comer said. “We have a duty to provide the accountability and transparency that Americans demand and deserve.”

The impeachment inquiry resolution does not accuse Mr. Biden of any wrongdoing. It authorizes three Republican-led panels to continue their investigations and petition a court for grand jury materials; authorizes subpoenas and retroactively approves a slew that have already been issued; and allows for the hiring of outside counsel to help with the inquiry.

Speaker Mike Johnson, who has accused Mr. Biden of corruption, said lawmakers are particularly focused on investigating four areas: the millions of dollars Hunter Biden and James Biden, the president’s brother, received from overseas business deals; false or misleading statements the elder Mr. Biden made about his son’s work; incidents in which the elder Mr. Biden met with or spoke with his son’s business partners; and about $240,000 the elder Mr. Biden received from his family members as reimbursement for loans.

Republicans have labored, so far without success, to prove that President Biden was enriched by his son’s business dealings. Many of the documents they have produced thus far have, in fact, demonstrated the opposite: that Mr. Biden lent money to his son and brother when they were in need, and they later paid him back.

The House Oversight Committee released documents that showed that one of Hunter Biden’s businesses, Owasco PC, made three payments of $1,380 to Joseph R. Biden Jr. in 2018 when he was not in office. Republicans said the payments were evidence of corruption. Other documents indicate the money was to pay back his father for helping to cover the cost of a Ford truck.

In a briefing with reporters, Mr. Jordan laid out his plan to call in nine more witnesses for questioning within two months.

In particular, Republicans are attempting to force two tax investigators to testify about why Hunter Biden wasn’t charged with felonies earlier. The Biden administration has made their bosses available to testify, but has balked at some of the Republicans’ demands, citing the lack of approval of the inquiry by the full House.

Mr. Jordan said Republicans were investigating whether Mr. Biden had taken a bribe, abused his power, engaged in other forms of misconduct or obstructed their investigation. Mr. Jordan suggested that false statements the president had made about his son’s business interests — such as his claim that Hunter Biden had not received any money from China — could constitute obstruction.

“We’ll look at all the facts and make a decision,” Mr. Jordan said. “Was it obstruction when Joe Biden said all the things he has said that turned out not to be accurate?”

On Wednesday, Hunter Biden said Republicans had invaded his privacy and savaged him personally for six years in the service of a false narrative about his father.

“They ridiculed my struggle with addiction; they belittled my recovery; and they have tried to dehumanize me — all to embarrass and damage my father, who has devoted his entire public life to service,” he said.

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