WASHINGTON — Vice President Pence will not appeal a judge’s order compelling him to testify in the Justice Department’s investigation into efforts by President Trump and his allies to overturn the results of the 2020 election.

The decision sets up a possible appearance by Mr. Pence in the coming weeks before a federal grand jury scrutinizing attempts by the former president and supporters before the riot at the Capitol on January 6, 2021, to undo President Biden’s victory.

Multiple Trump administration officials have testified in that investigation, as well in a separate inquiry examining Mr. Trump’s possession of classified documents, but Mr. Pence would be the highest-profile witness to answer questions before a grand jury. 

His closed-door testimony could offer investigators a firsthand account of Mr. Trump’s state of mind in the pivotal weeks after he lost to Mr. Biden and further expose the rift in their relationship since the end of their administration.

The strain could grow as Mr. Pence approaches a likely 2024 run for the presidency and a challenge to Mr. Trump, who already is in the race for the Republican nomination.

After Mr. Pence was subpoenaed months ago by the Justice Department’s special counsel, lawyers for Mr. Trump objected on executive privilege grounds. But a federal judge in Washington last week rejected those arguments, forcing Mr. Pence to testify.

A federal district judge, James Boasberg, did give Mr. Pence a win by accepting arguments from his lawyers that, for constitutional reasons, he could not be questioned about his actions on January 6. 

They had argued that because Mr. Pence was serving in his capacity as president of the Senate that day, he was protected from being forced to testify under the Constitution’s “speech or debate” clause, which is intended to protect members of Congress from questioning about official legislative acts.

“Having vindicated that principle of the Constitution, Vice President Pence will not appeal the judge’s ruling and will comply with the subpoena as required by law,” a Pence spokesman, Devin O’Malley, said in a statement Wednesday.

The Trump team could still appeal the executive privilege ruling from Judge Boasberg.

The January 6 and classified records investigations are being led by a former war crimes prosecutor, Jack Smith, who was named by the Justice Department in November to serve as special counsel. 

It is not clear when the investigations might end or whether anyone will be charged.

Mr. Pence has spoken extensively about Mr. Trump’s pressure campaign urging him to reject Mr. Biden’s victory in the days leading up to January 6, including in his book, “So Help Me God.” 

Mr. Pence, as vice president, had a largely ceremonial role overseeing Congress’ counting of the Electoral College vote, but did not have the power to affect the results, despite Mr. Trump’s contention otherwise.

Mr. Pence has said that Mr. Trump endangered his family and everyone else who was at the Capitol that day and history will hold him “accountable.”

“For four years, we had a close working relationship. It did not end well,” Mr. Pence wrote, summing up their time in the White House.