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

The judge’s comments in the civil case of the lawyer, John Eastman, marked a significant breakthrough for the House committee investigating the Jan. 6 attack on the Capitol. The committee, which is weighing making a criminal referral to the Justice Department, had used a filing in the case to lay out the crimes it believed Mr. Trump might have committed.

Mr. Trump has not been charged with any crime, and the judge’s ruling had no immediate, practical legal effect on him. But it essentially ratified the committee’s argument that Mr. Trump’s efforts to block Congress from certifying Joseph R. Biden Jr.’s Electoral College victory could well rise to the level of a criminal conspiracy.

“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 actions taken by Mr. Trump and Mr. Eastman, Judge Carter found, amounted to “a coup in search of a legal theory.”

The Justice Department has been conducting a wide-ranging investigation of the Capitol assault but has given no public indication that it is considering 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.

The judge’s ruling came as the committee was barreling ahead with its investigation. This week alone, people familiar with the investigation said, the panel has lined up testimony from four top Trump White House officials, including Jared Kushner, the former president’s son-in-law and adviser, whose interview was scheduled for Thursday.

The committee also voted 9-0 on Monday night to recommend criminal contempt of Congress charges against two other allies of Mr. Trump — Peter Navarro, a former White House adviser, and Dan Scavino Jr., a former deputy chief of staff — for their participation in efforts to overturn the 2020 election and their subsequent refusal to comply with the panel’s subpoenas. The matter now moves to the Rules Committee, then the full House. If it passes there, the Justice Department will decide whether to charge the men. A contempt of Congress charge carries a penalty of up to a year in jail.

But Judge Carter’s decision was perhaps the investigation’s biggest development to date, suggesting its investigators have built a case strong enough to convince a federal judge of Mr. Trump’s culpability and laying out a road map for a potential criminal referral.

Judge Carter’s decision came in an order for Mr. Eastman, a conservative lawyer who had written 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.

A lawyer for Mr. Eastman said in a statement on Monday that he “respectfully disagrees” with Judge Carter’s findings but would comply with the order to turn over documents.

In a statement hailing the judge’s decision, the chairman of the House committee, Representative Bennie Thompson, Democrat of Mississippi, and its vice chair, Representative Liz Cheney, Republican of Wyoming, said the nation must not allow what happened on Jan. 6, 2021, “to be minimized and cannot accept as normal these threats to our democracy.” Mr. Trump made no public statement about the ruling.

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 Jan. 6,” Judge Carter wrote.

One of the documents, according to the ruling, is an email containing the draft of a memo written for another one of Mr. Trump’s lawyers, Rudolph W. Giuliani, recommending that Mr. Pence “reject electors from contested states.”

“This may have been the first time members of President Trump’s team transformed a legal interpretation of the Electoral Count Act into a day-by-day plan of action,” 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 be charged with criminal violations including obstructing an official proceeding of Congress and conspiracy to defraud the American people.

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

“Dr. Eastman and President Trump launched a campaign to overturn a democratic election, an action unprecedented in American history,” he wrote.

In deciding that Mr. Trump and Mr. Eastman had “more likely than not” broken the law — the legal standard for determining whether Mr. Eastman could claim attorney-client privilege — Judge Carter noted that the former president had facilitated two meetings in the days before Jan. 6 that were “explicitly tied to persuading Vice President Pence to disrupt the joint session of Congress.”

At the first meeting, on Jan. 4, Mr. Trump and Mr. Eastman invited Mr. Pence and two of his top aides, Greg Jacob and Marc Short, to the Oval Office. There, Judge Carter wrote, Mr. Eastman “presented his plan to Vice President Pence, focusing on either rejecting electors or delaying the count.”

That meeting was followed by another, Judge Carter wrote, on Jan. 5, during which Mr. Eastman sought again to persuade Mr. Jacob to go along with the scheme.

Mr. Trump continued to pressure Mr. Pence even on Jan. 6, Judge Carter wrote, noting that the former president had made several last-minute appeals to Mr. Pence on Twitter. Mr. Trump called Mr. Pence by phone, Judge Carter wrote, and “once again urged him ‘to make the call’ and enact the plan.”

While the House committee has no authority to directly bring charges against Mr. Trump, and Mr. Trump was not a party to the Eastman civil case, Judge Carter’s ruling on Monday underscored the persistent questions of whether Mr. Trump could face criminal culpability for both his business dealings and his efforts to reverse the outcome of the election.

Last week, The New York Times reported that a prosecutor in New York City who was investigating Mr. Trump’s financial dealings believed the former president was guilty of “numerous felonies” in how he handled his real-estate and business transaction before taking office. The assessment of Mr. Trump by the prosecutor, Mark F. Pomerantz, came in a letter last month in which Mr. Pomerantz announced he was resigning from the Manhattan district attorney’s office, which had stopped pursuing an indictment of Mr. Trump.

Mr. Trump is also facing investigation from the district attorney in Atlanta who recently convened a special grand jury to help probe the former president’s attempts to overturn the 2020 election results in Georgia.

That inquiry centers on Mr. Trump’s actions in the two months between his election loss and Congress’s certification of the results, including a call he made to Brad Raffensperger, Georgia’s secretary of state, to pressure him to “find 11,780 votes” — the margin by which Mr. Trump lost the state.

The House committee has been seeking to assemble a definitive account of Mr. Trump’s efforts to hold on to the White House and how they led to the assault on the Capitol. Among the documents the committee will now receive from Mr. Eastman is an email that sketched “a series of events for the days leading up to and following Jan. 6, if Vice President Pence were to delay counting or reject electoral votes,” Judge Carter wrote.

The email “maps out potential Supreme Court suits and the impact of different judicial outcomes” were Mr. Pence to enact the plan.

The committee will also get documents related to state legislators who were involved in the effort to persuade Mr. Pence not to certify some electoral votes. One of them, Judge Carter wrote, is a letter from the Republican members of the Arizona legislature to Mr. Pence. Two others are letters from a Georgia state senator to Mr. Trump.

The committee has already heard from more than 750 witnesses. John McEntee, the former president’s personnel chief, testified Monday; Anthony Ornato, the former White House chief of operations, was scheduled to testify Tuesday; and Matthew Pottinger, former deputy national security adviser, will do so at a later date, those familiar with the investigation said.

Both Mr. Navarro and Mr. Scavino have argued they are prevented from testifying by Mr. Trump’s assertions of executive privilege, and that President Biden — who waived executive privilege for both men — does not have the authority to waive executive privilege over the testimony of a former president’s senior aide.