WASHINGTON — The House committee investigating the Jan. 6 attack on the Capitol said on Wednesday it would move forward with a criminal contempt of Congress referral against Mark Meadows, the former chief of staff for President Donald J. Trump, after he refused to appear for a scheduled deposition.

“The select committee is left with no choice but to advance contempt proceedings and recommend that the body in which Mr. Meadows once served refer him for criminal prosecution,” Representative Bennie Thompson, Democrat of Mississippi and the chairman of the committee, wrote to Mr. Meadows’s lawyer, George J. Terwilliger III.

The panel did not immediately announce a date to vote on a contempt referral, which is all but certain to be approved and sent to the full House, where lawmakers are likely to pass it, formally recommending that the Justice Department prosecute Mr. Meadows. It would be the third time the committee has moved to hold a recalcitrant witness in criminal contempt.

The committee has now interviewed more than 275 witnesses. Those cooperating include some members of former Vice President Mike Pence’s inner circle, including Marc Short, his former chief of staff. But several high-profile witnesses are stonewalling the panel, in line with a directive from Mr. Trump.

The former president is battling in court to block the release of documents requested by the committee that he says are subject to executive privilege, though the Biden administration has refused to assert that claim.

Mr. Meadows, who has turned over thousands of pages of documents to the committee, informed the panel on Tuesday that he was no longer willing to sit for a deposition that had been scheduled for Wednesday, reversing a deal he had reached with the panel just last week to be interviewed by its investigators. The leaders of the committee immediately threatened to charge Mr. Meadows, a former congressman from North Carolina, with contempt of Congress if he did not appear.

Mr. Thompson said Mr. Meadows had provided some useful information to the committee, including a November email that discussed appointing an alternate slate of electors to keep Mr. Trump in power and a Jan. 5 message about putting the National Guard on standby.

Mr. Meadows also turned over to the committee his text messages with a member of Congress in which the lawmaker acknowledged that a plan to object to Mr. Biden’s victory would be “highly controversial,” to which Mr. Meadows responded, “I love it.” And he furnished text exchanges about the need for Mr. Trump to issue a public statement on Jan. 6 aimed at persuading the mob marauding through the Capitol in his name to stand down.

But Mr. Meadows also informed the committee he had turned in the cellphone he used on Jan. 6 to his service provider, and he was withholding some 1,000 text messages connected with the device, Mr. Thompson said, prompting additional questions and the need for more cooperation and a deposition.

“There is no legitimate legal basis for Mr. Meadows to refuse to cooperate with the select committee and answer questions about the documents he produced, the personal devices and accounts he used, the events he wrote about in his newly released book and, among other things, his other public statements,” Mr. Thompson wrote.

The committee recently sent a flurry of subpoenas to telecommunications companies seeking the data of dozens of individuals, including Mr. Meadows, prompting his lawyer to object to a request he said sought “intensely personal communications” with no relevance to any legitimate investigation.

The subpoenas, which follow records preservation demands sent to 35 technology and social media companies in August, do not seek the content of any communications but simply the dates and times of when the calls and messages took place, according to a committee aide.

The House voted in October to recommend that another of Mr. Trump’s associates, Stephen K. Bannon, be charged with criminal contempt of Congress for refusing to cooperate with the investigation. A federal grand jury subsequently indicted him on two counts that could carry a total of up to two years behind bars. A judge on Tuesday set a July 18 trial date for Mr. Bannon, meaning that the select committee will most likely have to wait the better part of a year, if not longer, for a resolution of his case and any potential cooperation from him.

The committee has also recommended a contempt charge against Jeffrey Clark, a former Justice Department lawyer who participated in Mr. Trump’s efforts to invalidate the 2020 election results, for refusing to cooperate with its inquiry. The panel is waiting to complete that referral until it can determine how much information Mr. Clark is willing to provide during a deposition scheduled for Dec. 16. Mr. Clark has said he will invoke his Fifth Amendment right against self-incrimination.

Another potential witness, John Eastman, a lawyer who wrote a memo that some in both parties have likened to a blueprint for a coup to keep Mr. Trump in power, has also indicated that he plans to invoke the Fifth Amendment in response to the committee’s subpoena.

A third witness, the political operative Roger J. Stone Jr., told the committee this week that he, too, planned to invoke his right against self-incrimination in defying a subpoena, declining to sit for an interview or produce documents.

“Given that the select committee’s demand for documents is overbroad, overreaching and far too wide-ranging to be deemed anything other than a fishing expedition, Mr. Stone has a constitutional right to decline to respond,” his lawyer, Grant J. Smith, wrote to the panel.