The House select committee investigating the Capitol attack is asking Ivanka Trump, the daughter of the former president, to appear for a voluntary deposition to answer questions about Donald Trump’s efforts to stop the certification of Joe Biden’s election victory.

The move by the panel marks an aggressive new phase in its inquiry into the 6 January insurrection, as House investigators seek for the first time testimony from a member of the Trump family about potential criminality on the part of the former president.

Congressman Bennie Thompson, the chair of the select committee, said in an 11-page letter to Ivanka Trump that the panel wanted to ask about Trump’s plan to stop the certification, and his response to the Capitol attack, including delays to deploying the national guard.

Ivanka Trump was a senior adviser to her father during her presidency, as was her husband Jared Kushner. The two were seen as a power couple very close to the inner workings of the Trump White House.

The questions to Ivanka appear directed at a key issue: whether her father oversaw a criminal conspiracy on 6 January that also involved obstructing a congressional proceeding – a crime.

The letter said that the panel first wanted to question Ivanka Trump about what she recalled of a heated Oval Office meeting on the morning of the 6 January insurrection when the former president was trying to co-opt Mike Pence into rejecting Biden’s win.

The former president was on the phone with the then vice-president in an Oval Office meeting with Ivanka and Keith Kellogg, a top Pence aide, the letter said. When Pence demurred on the former president’s repeated request, Ivanka turned to Kellogg and said Pence was “a good man”.

Thompson said in the letter that the panel wanted to learn more about that exchange with Pence she heard, as well as other conversations about impeding the electoral count at the joint session of Congress on 6 January that she may have witnessed or participated in.

“The committee has information suggesting that President Trump’s White House counsel may have concluded that the actions President Trump directed Vice-President Pence to take would … otherwise be illegal. Did you discuss these issues?” the letter said.

Thompson added House investigators had additional questions about whether Trump could shed light on whether the former president had been told that such an action might be unlawful, and yet nonetheless persisted in pressuring Pence to reinstall him for a second term.

The letter said the select committee was also interested in learning more from Trump about her father’s response to the Capitol attack on 6 January, and discussions inside the White House about the former president’s tweet castigating Pence for not adopting his plan.

Thompson said the nagging question for Ivanka Trump – who White House aides thought had the best chance of having the former president condemn the rioters – was what she did about the situation and why her father did not call off the rioters in a White House address.

The select committee said in the letter that they also wanted to ask her about what she knew with regard to the long delay in deploying the national guard to the Capitol, which allowed the insurrection to overwhelm law enforcement into the afternoon of 6 January.

Thompson said that House investigators were curious why there appeared to have been no evidence that Trump issued any order to request the national guard, or called the justice department to request the deployment of personnel to the Capitol.

Speaking to the Guardian and a small group of reporters on Thursday, the chairman of the select committee said that the immediate focus for the investigation was on the former president’s daughter and not subpoenas to Republican members of Congress.

Thompson said the panel would be “inviting some people to come and talk to us. Not lawmakers right now. Ivanka Trump.”

The letter comes after the US supreme court, in another blow to the former president, late on Wednesday rejected his request to block the release of more than 700 of the most sensitive of White House documents he had tried to hide from the select committee.

The former president’s defeat means those documents – including presidential diaries, notes and memos from the files of top aides including the former White House chief of staff Mark Meadows – that could shed light on the Capitol attack can now be transferred to Congress.