The representative said Cuccinelli, a DHS official during the Trump administration, was asked about the events of Jan. 6 and the agency's preparations for that day. He was also asked about his interactions with former President Donald Trump and ex-White House chief of staff Mark Meadows during an interview that lasted four-and-a-half hours, the representative said.
Cuccinelli toured the Capitol on the night of Jan. 6 to survey the damage after rioters left the building.
CNN first reported Cuccinelli's interactions with the House committee.
Cuccinelli, a former attorney general for Virginia, was a key fixture in the Trump administration, advancing some of the former president's hardline immigration policies.
In a 400-page report released in October by the Senate Judiciary Committee, Trump was said to have floated the idea of appointing Cuccinelli as a special counsel to investigate claims of election fraud.
In recent weeks, the Jan. 6 committee has ramped up its pressure on key Trump allies and former administration officials. The House voted this week to refer Meadows to the Justice Department for a potential criminal charge over his refusal to answer questions about the Jan. 6 attack on the U.S. Capitol.