Mr. Rosen declined to comment. A spokesman for Mr. Trump could not immediately be reached for comment.
The documents “show that President Trump tried to corrupt our nation’s chief law enforcement agency in a brazen attempt to overturn an election that he lost,” said Representative Carolyn B. Maloney, a New York Democrat who is the chairwoman of the House Oversight Committee.
Ms. Maloney, whose committee is looking into the events leading up the Jan. 6 storming of the Capitol by a pro-Trump crowd protesting the election results, including Mr. Trump’s pressure on the Justice Department, said she has asked former Trump administration officials to sit for interviews, including Mr. Meadows, Mr. Clark and others. The House Oversight Committee requested the documents in May as part of the inquiry, and the Justice Department complied.
The draft brief that Mr. Trump wanted the Justice Department to file before the Supreme Court mirrored a lawsuit that Attorney General Ken Paxton of Texas had filed to the court, alleging that a handful of battleground states had used the pandemic to make unconstitutional changes to their election laws that affected the election outcome. The states argued in response that Texas lacked standing to file the suit, and the Supreme Court rejected the case.
The version of the lawsuit that Mr. Trump wanted the Justice Department to file made similar claims, saying that officials in Georgia, Michigan, Wisconsin, Arizona, Nevada and Pennsylvania had used the pandemic to unconstitutionally revise or violate their own election laws and weaken election security.
To try to prove its case, the lawsuit relied on descriptions of an election monitoring video that appeared similar to one that Republican officials in Georgia rejected as doctored, as well as the debunked notion, promoted by Mr. Trump, that machines made by Dominion Voting Systems had been hacked.
Eager to speak with Mr. Rosen about the draft Supreme Court lawsuit, a lawyer named Kurt Olsen, who had advised on Mr. Paxton’s effort, tried unsuccessfully to reach him multiple times, according to emails sent between 11 a.m. and 10 p.m. on Dec. 29 and obtained by the House Oversight Committee investigators.