Republican and Democrat leaders on the House of Representatives Intelligence Committee are threatening a subpoena unless the White House clarifies whether any recordings, memoranda or other documents exist of Donald Trump's meetings with sacked FBI director James Comey.
The panel had previously set a June 23 deadline for the White House to respond to its request.
The day before, President Trump said in a series of tweets that he "did not make, and do not have, any such recordings", but also said he had "no idea" if tapes or recordings of his conversations with Mr Comey existed.
The White House then responded to the committee request by referring to Mr Trump's tweets.
The committee had asked for any recordings after Mr Trump suggested there may be tapes just days after he fired Mr Comey, who was leading an investigation into Trump associates' ties to Russian officials.
Mr Trump has disputed Mr Comey's assertion that the president asked him for a pledge of loyalty during a dinner meeting.
When news of Mr Comey's account broke, Mr Trump tweeted that Mr Comey "better hope that there are no 'tapes' of our conversations before he starts leaking to the press!".
A letter on Thursday from Republican congressman Mike Conaway of Texas, who is leading the Russia probe, and California Democrat Adam Schiff, says Mr Trump's June 22 Twitter statement "stops short of clarifying" whether the White House has any tapes or documents.
Mr Conaway and Mr Schiff said in a statement that the letter makes clear that should the White House not respond fully, "the committee will consider using compulsory process to ensure a satisfactory response".
The panel is investigating Russian intervention in the 2016 elections, including any possible links to the Trump campaign.
Interviews set for July include former national security adviser Susan Rice, who asked government analysts to disclose the name of Trump associates documented in intelligence reports.
She has firmly denied that she did anything inappropriate, but Mr Trump has said she may have committed a crime.
On Thursday, her spokeswoman Erin Pelton said Ms Rice "is co-operating with the bi-partisan Russia investigations conducted by the intelligence committees, as she said she would".
Meanwhile Democrats on two House committees asked the Justice Department's inspector general to investigate whether attorney general Jeff Sessions violated his recusal from the Russia probe by taking part in Mr Comey's sacking in May.
House Oversight and Judiciary Committee Democrats urged Michael Horowitz to examine "a lapse in judgment".
Mr Sessions insisted in an appearance before the Senate intelligence committee this month that he had not violated his decision in March to recuse himself from any investigation related to inquiries involving Mr Trump's 2016 campaign.
During his evidence, Mr Sessions said it would be "absurd" to suggest a recusal from a single investigation would render him unable to manage leadership of the FBI.