The House select committee investigating the deadly assault on the US Capitol on 6 January is prepared to urge federal prosecution of former aides to Donald Trump who refuse to comply with subpoenas, a key panel member said.

Former White House chief of staff Mark Meadows, deputy chief of staff Dan Scavino, strategist Steve Bannon and Pentagon aide Kash Patel are defying subpoenas for documents and testimony, under instruction from the former president.

Amid fears that the panel will not seek to enforce its will, Adam Schiff, a member of the panel as well as chairman of the House intelligence committee, spoke to CBS’s Face the Nation on Sunday.

The 6 January committee, the California congressman said, “wants to make sure that these witnesses come in and testify, and we are prepared to go forward and urge the justice department to criminally prosecute anyone who does not do their lawful duty”.

Liz Cheney of Wyoming, one of only two Republicans on the committee, has also said it will enforce subpoenas.

Schiff also greeted a decision by the Biden administration not to invoke executive privilege over documents pertaining to the Capitol attack.

The riot, around which five people including a police officer died, followed a rally near the White House at which Trump exhorted followers to “fight like hell” to overturn his election defeat.

Schiff said he hoped the House committee would see such materials “very soon”.

“I applaud the Biden administration for not asserting executive privilege,” he said, “not trying, because it’s protecting its own prerogative, to deprive the American people of the full facts. So hats off to the administration.

“We should I think get those documents soon because the sitting president has the primary say on executive privilege.”

On Friday, in a letter announcing their client’s decision not to comply with his subpoena, attorneys for Bannon attempted to assert executive privilege themselves. Observers pointed out that executive privilege applies to communications involving the president the White House wishes to keep confidential – but though Trump was in power on 6 January, Bannon was not working for him.

Trump repeated the lies about electoral fraud which fuelled the attack at a rally in Des Moines, Iowa, on Saturday. Two senior Republicans, Senator Chuck Grassley and Governor Kim Reynolds, stood with him.

Referring to a Senate judiciary committee majority report this week about how Trump pressured his acting attorney general before the Capitol attack, Schiff said: “We saw Grassley [the senior Republican on the judiciary committee] in Iowa yesterday, unable to condemn the president’s effort to to get the justice department to overturn the election.”

Referring to Steve Scalise of Louisiana, the House Republican whip, Schiff pointed to “another Republican leader unable to acknowledge that the election wasn’t stolen”. On Fox News Sunday, Scalise refused three times to say if he believed the election was stolen.

“It’s these personal capitulations that are putting our country at risk,” Schiff said, adding that the Republican party “is now an autocratic cult around Donald Trump … not interested in governing”.

Trump’s Iowa rally was part of a shadow campaign. The former president remains eligible to run for the White House because enough Republican senators stayed loyal in his second impeachment trial, for inciting the Capitol attack, to stave off conviction. But Trump has not formally declared a run.

Speaking to NBC’s Meet the Press, the Rhode Island senator Sheldon Whitehouse, a Democrat, said the American people should see Trump aides testify under oath.

“When you consider that these were Trump appointees,” Whitehouse said, of events before the 6 January rally outlined in the Senate judiciary committee report, “people who are willing to go right to the chalk line, and in my view, even over it, when those folks saw this as outlandish and illegal and something that they don’t quit before they participate in, that shows how berserk this had gotten.”

Referring to Jeffrey Clark, a senior justice department lawyer whose willingness to help Trump was outlined in the Senate report, Whitehouse said: “We then go on to the further question of, ‘OK, how was this organised? Was this really just one little guy in the Department of Justice with a wild idea?’ I doubt it.”

Observers including the comedian Bill Maher have warned of a “slow-moving coup”, shorthand for processes by which Republicans at state levels have since 2020 moved to change voting and electoral laws and to install sympathetic officials in positions which monitor and certify elections.

The former White House press secretary Stephanie Grisham, author of a tell-all book about her former boss, also appeared on NBC on Sunday.

She said that if Trump “does run again in 2024, he’ll have no guardrails because he will never have to worry about re-election, so he will do whatever he wants. He will hire whomever he wants. And I think that includes people of the 6 January mind … imagine who he could put into the DoJ in 2024, knowing he’s got no consequences there.”

Asked if Trump would “destroy the democracy”, Grisham said: “I think it will be a very terrifying time.

“I think it will be nothing but revenge, retribution and how he can benefit himself. There will be pardons happening. I think there will be very draconian policies that go way too far. So I believe if he is re-elected it will be a really, really scary time.”