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The attack on the Capitol by Trump supporters took place as Congress met to certify Democrat Joe Biden's election victory over Trump, delaying that process for several hours as then-Vice President Mike Pence, members of Congress, staff and journalists fled.
More than 600 people face criminal charges stemming from the event. Five people died as a result of the rampage.
Trump asserted in the lawsuit filed in US District Court for the District of Columbia on Monday that materials sought by the select committee are protected by a legal doctrine called executive privilege, which protects the confidentiality of some White House records.
The lawsuit seeks an injunction against the panel's request for materials.
Meanwhile, the committee has told Steve Bannon it rejects his arguments for failing to cooperate with the probe, as the panel pursues a contempt of Congress charge against the long-time adviser to Trump.
Trump has claimed that his communications with aides are protected by executive privilege, a legal doctrine that protects the confidentially of some White House communications. But legal experts have said he cannot lawfully use executive privilege because he is now the former president.
In a letter to Bannon's attorney dated Friday and seen by Reuters on Monday, Representative Bennie Thompson, chairman of the House of Representatives Select Committee, dismissed that claim.
The letter was first reported by The Washington Post.
The Select Committee is scheduled to meet on Tuesday evening to vote on a report recommending that the House cite Bannon for criminal contempt of Congress and refer him to the US Attorney for the District of Columbia for prosecution.
Thompson wrote that Trump has not communicated any such assertion of executive privilege, formally or informally, to the committee.
"Moreover, we believe that any such assertion of privilege -should it be made by the former President - will not prevent the Select Committee from lawfully obtaining the information it seeks," Thompson wrote.
Bannon's attorney, Robert Costello, did not immediately respond to a request for comment on the letter.