Bipartisan figures on the congressional committee investigating Donald Trump’s attempts to overturn his 2020 election defeat said on Sunday they expected the former president’s close ally, Rudolph Giuliani, would comply with a subpoena to give testimony.

Giuliani is among a number of Trump sphere insiders who have so far refused to cooperate with the bipartisan House panel looking into Trump’s subversion efforts and the January 6 Capitol insurrection the then president incited that claimed five lives. Giuliani was scheduled to testify last Tuesday, after the committee issued a subpoena last month, but did not appear.

Elaine Luria, a Virginia Democratic congresswoman and member of the select committee, said Giuliani had already been in touch, seeming to confirm the substance of a New York Times report that Giuliani was in talks about options including an in-person interview or submitting a deposition.

“He has been in contact with the committee,” she told MSNBC of Giuliani. “He had an appearance that has been rescheduled but he remains under subpoena and we expect him to cooperate fully with the investigation.”

And Adam Kinzinger, an Illinois Republican and committee member, indicated in an appearance on CBS that he was of the understanding, also, that Giuliani would comply.

“He’s been subpoenaed [and] our expectation is he was going to cooperate, because that’s the law, same as someone subpoenaed to court,” Kinzinger told CBS’s Face the Nation.

He added: “There may be some changes in dates and moments here, as you know, lawyers do their back and forth, but we fully expect that in accordance with the law, we’ll hear from Rudy.

“But regardless of when we hear from Rudy, or how long that interview is, we’re getting a lot of information and we’re looking forward to wrapping this up at some point.”

Giuliani was prominent in Trump’s failed plotting to hold on to power and prevent Joe Biden taking office, and is reported to have been at the center of an unprecedented plan to order the Department of Homeland Security to seize voting machines in contested states.

The Times report notes that Giuliani has not yet agreed to cooperate, but the specter of his evidence about maneuverings inside the White House during the final weeks and days of the Trump administration is another milestone moment in an already turbulent week for the former Republican president.

The Washington Post reported on Thursday that Trump took boxes of records, including top secret documents, to Mar-a-Lago, his Florida retreat, when he left office, in possible violation of government record-keeping laws.

And an upcoming book from New York Times journalist Maggie Haberman claims that Trump periodically clogged White House toilets by attempting to flush away printed papers. Trump has denied the allegations.

In recent days, meanwhile, several senior Republicans have criticized the party’s censure of Kinzinger and Wyoming congresswoman Liz Cheney for serving on the committee, and the Republican National Committee’s controversial characterization of the riot as “legitimate political discourse”.

Mike Pence, Trump’s vice-president, called Trump’s efforts to overturn the election “un-American” at a conservative conference in Florida, while on Friday the Senate minority leader Mitch McConnell added his voice to the growing Republican backlash against Trump’s big lie that the November 2020 election was stolen from him by the Democrats.

“It was a violent insurrection for the purpose of trying to prevent the peaceful transfer of power after a legitimately certified election, from one administration to the next,” McConnell said of the January 6 riot, adding that it was “not the job” of the Republican party to single out members “who may have different views from the majority.”

Larry Hogan, the Republican governor of Maryland and a frequent Trump critic, also slammed the RNC’s position over the insurrection.

“To say it’s legitimate political discourse to attack the seat of our capital, and smash windows and attack police officers, and threaten to hang the vice-president and threaten to overthrow the election, it’s insanity,” he told CNN’s State of the Union show on Sunday.

“The Republican party I want to get back to is the one that believes in freedom and truth and not one that attacks people who don’t swear 100% fealty to the ‘Dear Leader’ [Trump].”

Giuliani, if he testifies, could impart invaluable first-hand knowledge of Trump’s plotting, although the Times notes that negotiations could yet fall apart.

Its report cites three anonymous sources stating that Giuliani has had talks with the committee about the format and content of his possible testimony, including how much of his interaction with Trump he would yet look to shield under attorney-client privilege.

The article suggests Giuliani could be seeking to avoid a costly legal fight and trying to evade a criminal referral for contempt of congress, by dangling a promise of testimony.

In November, Steve Bannon, a former Trump adviser, pleaded not guilty to criminal contempt of Congress for his refusal to comply with a committee subpoena, while the House of Representatives has recommended charges for former Trump White House chief of staff Mark Meadows.

Kinzinger, who will not seek re-election in this year’s midterm elections, also believes senior party figures such as Pence and McConnell speaking out could help provide “political cover” for anti-Trump Republican candidates.

“I don’t care if you’re running for city council, Congress, Senate, etc, every Republican has to be clear and forceful on the record, do they think January 6th was legitimate political discourse?” he asked.