The special US House committee investigating the January 6 Capitol attack is weighing whether to issue a contempt of Congress referral for Donald Trump after the former president skipped a closed-door deposition with the panel that was scheduled for Monday.

The committee’s Democratic chair, Bennie Thompson, said that the contempt of Congress referral targeting Trump “could be an option” – though the Mississippi congressman added that the panel would have to first address a lawsuit filed against it by Trump’s lawyers on Friday. The suit challenged the subpoena ordering Trump to appear at the deposition as a violation of executive privilege.

In a joint statement with Liz Cheney, the outgoing Republican congresswoman and vice-chair of the committee, Thompson said that Trump’s lawsuit “parades out many of the same arguments that courts have rejected repeatedly over the last year”.

“The truth is that Donald Trump, like several of his closest allies, is hiding from the select committee’s investigation and refusing to do what more than a thousand other witnesses have done,” which is to testify in accordance with panel-issued subpoenas, they said.

Four Trump allies have already been held in contempt of Congress after refusing to comply with committee subpoenas.

The US justice department has declined to charge two who were held in contempt of Congress: former White House chief of staff Mark Meadows and former deputy chief of staff Dan Scavino.

Two others, Steve Bannon and Peter Navarro, were indicted. Navarro’s trial is scheduled for January while Bannon was found guilty by a jury and was sentenced to four months in prison as well as a fine of $6,500. Bannon earlier this month appealed the trial and sentence.

With Republicans on Tuesday sitting on the cusp of getting majority control in the House after the recent midterm elections, the committee will dissolve in January.

Along with the pressure from the January 6 committee, Trump has also been facing attacks from fellow Republicans over the midterm election as several of his endorsed candidates failed to win their races. Trump is expected to announce his candidacy for the 2024 presidential race, though any signs of strong support from his party have been dim.

A new poll from conservative group Club for Growth, once a Trump ally, showed Trump polling behind Florida’s Republican governor, Ron DeSantis, by double digits in hypothetical runs in Iowa and New Hampshire.

In an interview with ABC News released on Monday, Trump’s former vice-president, Mike Pence, said that the US would have “better choices in the future” than Trump. Pence said that he and his family are taking “prayerful consideration” of whether he should run himself in 2024.

“People in this country actually get along pretty well once you get out of politics,” Pence said. “And I think they want to see their national leaders start to reflect that same compassion and generosity of spirit.

“So in the days ahead, I think there will be better choices.”