President asked then-FBI chief James Comey to end inquiry on former national security advisor's Russia ties
"I hope you can let this go," Trump told Comey, according to Comey's personal memos first reported by the New York Times newspaper and corroborated by the Washington Post.
Comey wrote the two-page long notes after a meeting in February with the president, according to Comey associates anonymously quoted by both newspapers.
Late Tuesday, the Republican head of the House Oversight Committee demanded the FBI hand over all documents related to any discussions between Trump and Comey.
Jason Chaffetz sent the letter to the bureau just hours after the Times’ report was published.
Trump abruptly fired the FBI chief last week, citing his handling of 2016 presidential candidate Hillary Clinton's email scandal.
Comey's dismissal came amid an ongoing FBI investigation into whether Trump campaign associates colluded with Russia in last year's election.
That has prompted many, including from within his own party, to question the president's rationale for firing the FBI chief.
The reports Tuesday' are likely to spur further speculation the president is trying to shield his election campaign from scrutiny regarding its ties to Russian officials.
A day after Comey was fired, the Senate Intelligence Committee subpoenaed Flynn for documents pertaining to his communications with Russian officials.
The subpoena came after Flynn declined to cooperate with the committee’s request last month for documents, according to chairman Sen. Richard Burr and vice chai Sen. Mark Warner.
The committee is conducting an investigation into Moscow's alleged meddling in the presidential election.
Less than a month after appointing him, Trump fired Flynn for misleading Vice President Mike Pence and senior administration officials regarding the nature of his interactions with Russia's ambassador to the U.S., according to the White House.
Flynn offered in March to testify before congressional intelligence committees in exchange for immunity from prosecution, but his offer was rejected.