Separately, the New York Times reported on Friday that Trump told Russian officials at a White House meeting last week that firing Comey relieved "great pressure" that the president was facing from the ongoing probe into Russia and the election.
Comey has agreed to testify before the Senate intelligence committee, although a date has not yet been set, according to the committee's chairman, Senator Richard Burr.
Mr Trump's terse denial followed reports by Reuters and other media about a memo written by Mr Comey alleging that Mr Trump made the request to close down the investigation into Mr Michael Flynn and Russian Federation in February.
Ex-FBI director James Comey has agreed to testify openly to the Senate on alleged Russian meddling in the 2016 U.S. election. The news broke as the Washington Post reported that the investigation had identified a senior current White House official as a "significant person of interest".
But uproar in Washington threatened to cast a long shadow, after Mr Comey's firing, allegations Mr Trump had previously pressed the Federal Bureau of Investigation chief to stop investigating former national security adviser Michael Flynn, and the subsequent appointment of a special counsel to look into alleged Russian meddling in the 2016 election and possible ties to Mr Trump's campaign. The S&P 500 finished up 0.67%, the Dow Jones Industrial Average rose 0.68% and the Nasdaq gained 0.47%.
And in the meeting with the Russians, he said, "I faced great pressure because of Russia". Let me just share part of what [White House press secretary] Sean Spicer had to say in particular about that Washington Post story, the suggestion that the Russian Federation probe is now involving current White House officials at the highest level of government.More news: Mourinho names United's youngest ever Premier League line-up
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Trump denied that charge at a press conference on Thursday. In his briefings with lawmakers, Rosenstein said that he knew Trump was going to fire Comey prior to writing the memo in question, according to McClatchy.
Former FBI chief Robert Mueller was named special counsel last week to investigate alleged Russian interference in the 2016 USA election and possible collusion between Trump's campaign and Moscow.
It has also been reported that Trump had told the Russians classified information about military operations involving Isis.
House minority leader Nancy Pelosi said Trump has shown his disrespect for the presidency if the Times report is accurate. It says the president then told Russia's foreign minister and ambassador that he "faced great pressure because of Russian Federation". Mueller's former law firm, WilmerHale, represents Kushner - who has been in the spotlight over the president's decision to fire James Comey from the FBI and for meeting with Russian officials - and Manafort, who is now under federal investigation.
In the Oval Office weeks later, Mr Comey told associates, the President asked him to shut down an investigation into former national security adviser Michael Flynn.
The White House has not denied the reports.