WASHINGTON — A federal judge ruled on Monday that former President Donald J. Trump and a lawyer who advised him on how to overturn the 2020 election most likely committed felonies, including obstructing the work of Congress and conspiring to defraud the United States.

The judge’s comments marked a significant breakthrough for the House committee investigating the Jan. 6 attack on the Capitol, which had laid out in a civil filing the crimes it believed Mr. Trump might have committed as it weighs making a criminal referral to the Justice Department.

“The illegality of the plan was obvious,” wrote Judge David O. Carter of the Central District of California. “Our nation was founded on the peaceful transition of power, epitomized by George Washington laying down his sword to make way for democratic elections. Ignoring this history, President Trump vigorously campaigned for the vice president to single-handedly determine the results of the 2020 election.”

The Justice Department has been conducting a wide-ranging investigation of the Capitol assault but has given no public indication that it is considering pursuing a criminal case against Mr. Trump. A criminal referral from the House committee could increase pressure on Attorney General Merrick B. Garland to do so.

Judge Carter’s comments came in an order for John Eastman, a conservative lawyer who wrote a memo that members of both parties have likened to a blueprint for a coup, to turn over more than 100 emails to the committee as it investigates Mr. Trump’s efforts to hold onto power after his election loss.

Many of the documents the committee will now receive relate to a legal strategy proposed by Mr. Eastman to pressure Vice President Mike Pence not to certify electors from several key swing states when Congress convened on Jan. 6, 2021. “The true animating force behind these emails was advancing a political strategy: to persuade Vice President Pence to take unilateral action on January 6,” Judge Carter wrote.

Mr. Eastman had filed suit against the panel, trying to persuade a judge to block the committee’s subpoena for documents in his possession. As part of the suit, Mr. Eastman sought to shield from release documents he said were covered by attorney-client privilege.

In response, the committee argued — under the legal theory known as the crime-fraud exception — that the privilege did not cover information conveyed from a client to a lawyer if it was part of furthering or concealing a crime.

The panel said its investigators had accumulated evidence demonstrating that Mr. Trump, Mr. Eastman and other allies could potentially be charged with criminal violations including obstructing an official proceeding of Congress and conspiracy to defraud the American people.

On Monday, Judge Carter, who was nominated by President Bill Clinton, agreed, writing that he believed it was “likely” that the men not only conspired to defraud the United States but “dishonestly conspired to obstruct the joint session of Congress on Jan. 6, 2021.”

“President Trump and Dr. Eastman justified the plan with allegations of election fraud,” he wrote, “but President Trump likely knew the justification was baseless, and therefore that the entire plan was unlawful.”