The former president had battled to keep secret the information on activity surrounding the U.S. Capitol riot.
The panel is demanding info and testimony from people who allegedly submitted false Electoral College certificates declaring Trump the winner of Arizona, Georgia, Michigan, New Mexico, Nevada, Pennsylvania and Wisconsin.
Select committee Chair Bennie Thompson was asked about reports Trump was presented with a draft executive order to seize voting machines.
The Republican lawmaker was in touch with Donald Trump the day of the Capitol riot, and the committee wants to know what they talked about.
"When a president refuses to tell the mob to stop, when he refuses to defend any of the coordinate branches of government, he cannot be trusted,” she said.
Information from Mark Meadows "has been quite revealing about members of Congress involved in the activities of Jan. 6,” said Rep. Bennie Thompson.
Trump's former chief of staff has "produced records to the committee and will soon appear for an initial deposition," the committee stated.
Rep. Bennie Thompson said that if lawmakers investigating the attack find enough evidence against Trump, "We will go forward with it."
Bannon is refusing to comply with a subpoena from the nine-member House select committee investigating the Jan. 6 attack.
“Nothing is off-limits,” said Rep. Bennie Thompson, who has been tapped as chairman of the House Homeland Security Committee.