In a memo written in February, Comey wrote that Trump asked him during a one-on-one meeting to stop investigating former national security adviser Michael Flynn, The Times reported.
The US Department of Justice named a former head of the FBI as special counsel to lead the investigation into alleged Russian meddling in the 2016 election and possible collusion with Donald Trump's team.
"No politician in history, and I say this with great surety, has been treated worse or more unfairly", he said on Wednesday to the United States Coast Guard Academy.
Following Comey's firing, Democrats have clamored for an investigation that would be seen as less partisan.
Mr Comey's memo, an apparent effort to create a paper trail of his contacts with the White House, would be the clearest evidence to date that the president has tried to influence the investigation.
Trump is both publicly and privately stewing about Deputy Attorney General Rob Rosenstein's decision to name special counsel.
The Comey memo's emergence had congressional Democrats suggesting that the president engaged in obstruction of justice, an impeachable offence. House Republicans had mixed reactions to the announcement. The FBI is investigating to determine whether Trump or his associates colluded with Russian Federation, although no evidence to support the allegation has surfaced.
Republicans in Congress are trying to project a business-as-usual approach amid the chaos.
In addition Mr Trump is facing pointed questions about his discussions with Russian diplomats during which he is reported to have disclosed classified information.
"As long as Congress does its job under the Constitution, nothing is going to stall", said Senate Judiciary Chairman Chuck Grassley of Iowa. "We don't have to wait for a president; in fact a lot of people in Congress get irritated when presidents interfere".
In previous months, Republican lawmakers were more likely to fully defend Trump - even after he and his administration made comments and policy changes that generated intense criticism.
"A special prosecutor is the first step, but it can not be the last".
The Reporters Committee for Freedom of the Press responded to Trump's suggestion to imprison members of the media, saying in a statement that it "should not intimidate the press but inspire it", according to CNBC. "A special prosecutor does not negate the need for vigorous Congressional investigations either", Pelosi said in a statement.