House Oversight Committee chair Jason Chaffetz demanded that all correspondence be presented by 24 May.
US media have quoted a memo by Mr. Comey that reportedly says Mr. Trump asked him to drop an inquiry into links between his ex-national security adviser Michael Flynn and Russia.
The White House denied the allegation.
"The president has never asked Mr. Comey or anyone else to end any investigation, including any investigation involving General Flynn," it said.
Mr. Trump fired Mr. Comey last week in a move that stunned Washington.
Meanwhile, Russian President Vladimir Putin promised to release to Congress records of a White House meeting between Mr. Trump, Russian Foreign Minister Sergei Lavrov and Russian Ambassador Sergei Kislyak.
Mr. Putin said Mr. Trump had passed on no secrets at the meeting.
Critics have questioned the timing of the meeting, which came a day after Mr. Comey was sacked, and on Tuesday US media quoted officials as saying Mr. Trump had passed on classified information there.