In an Oval Office meeting with senior Russian officials last week, Trump called Comey a "nut job" and said firing the intelligence chief had relieved "great pressure" on him, The New York Times reported.
The exchange supports claims that Trump sacked Comey over the bureau's probe into possible collusion between the real estate mogul's campaign and Moscow.
The Washington Post meanwhile said the FBI has identified an unnamed senior White House official as a "significant person of interest" in its sprawling probe of Russian meddling in the 2016 presidential election.
The reports came just as Trump flew to Saudi Arabia to kick off his first foreign trip as US leader -- highlighting how the controversy over his team's alleged links to Moscow is dogging his fledgling presidency.
Comey will testify in open session of the Senate Intelligence Committee at some point after the Memorial Day holiday, May 29, though a date has not yet been set.
The ex-FBI chief has not spoken publicly since his surprise firing last week.
"I am hopeful that he will clarify for the American people recent events that have been broadly reported in the media," panel Chairman Richard Burr said in a statement.
The top Democrat on the Senate Intelligence Committee, Mark Warner, said he expects Comey to "shed light on issues critical to this Committee's investigation of Russian interference in the 2016 election."
However, members of the Senate Judiciary Committee said Comey declined their invitation to testify before the panel over the circumstances surrounding his abrupt removal.
"We're extremely disappointed in James Comey's decision not to testify voluntarily before the Judiciary Committee," said Chairman Chuck Grassley and the panel's top Democrat, Dianne Feinstein, urging Comey to reconsider.
"There is no reason he can't testify before both the Intelligence and Judiciary Committees... Given his commitment to the people and the mission of the FBI, we expected him to be responsive to the senators responsible for vetting its next proposed leader."
The White House has been thrown into turmoil by a succession of stunning allegations against the president this week, including that he may have obstructed justice by asking Comey to drop an investigation into one of his top advisors.
- Moscow ties under microscope -
The latest report from the Post, citing unnamed sources familiar with the investigation, undercuts Trump's insistence that his campaign had nothing to do with the Kremlin.
Trump's national security advisor Michael Flynn was forced to resign for misleading Vice President Mike Pence about a phone call with the Russian ambassador.
"I just fired the head of the FBI. He was crazy, a real nut job," Trump told Russian Foreign Minister Sergei Lavrov last week, according to the Times, citing notes taken at the meeting and read to the paper by a US official.
"I faced great pressure because of Russia. That's taken off."
That flies in the face of the White House's public insistence that Comey's dismissal was not linked to his ongoing investigation.
White House spokesman Sean Spicer did not dispute the Times's account.
Intercepted Russian communications suggest that Russian officials felt that they had built up such a strong relationship with Flynn that they could use him to influence Trump and his inner circle, CNN reported.
It cited current and former administration officials as saying US intelligence officials were so concerned about the conversations between Flynn and the Russians that they would limit how much sensitive information they shared with him.
- Did he or didn't he? -
On Thursday, Trump declared himself the victim of the "greatest witch hunt" in American political history and denied allegations of collusion.
"There is no collusion between certainly myself and my campaign, but I can always speak for myself, and the Russians -- zero," Trump told reporters.
The White House on Friday predicted that the investigation would back up Trump's account.
"As the president has stated before -- a thorough investigation will confirm that there was no collusion between the campaign and any foreign entity," said Spicer.
Spicer offered a new explanation for the firing, saying that Trump had been trying to improve relations with Russia -- and Comey got in the way.
"By grandstanding and politicizing the investigation into Russia's actions, James Comey created unnecessary pressure on our ability to engage and negotiate with Russia," he said.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)