Reports have emerged that Mr Comey wrote a memo after a meeting with Mr Trump, where the US President was quoted as saying "I hope you can let this go".
"The Committee looks forward to receiving testimony from the former Director on his role in the development of the Intelligence Community Assessment on Russian interference in the 2016 United States elections, and I am hopeful that he will clarify for the American people recent events that have been broadly reported in the media", said Burr, who chairs the committee.
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.
While the White House initially pointed to a memo from Deputy Attorney General Rod Rosenstein, outlining Comey's mismanagement of the investigation into Democratic presidential nominee Hillary Clinton's private email server, as the impetus for his termination, Trump later admitted that the Russian Federation investigation - which he has called a "hoax" - played a role.
"As the president has stated before - a thorough investigation will confirm that there was no collusion between the campaign and any foreign entity", White House spokesman Sean Spicer said in a statement in response to the Post report.
"Director Comey ... deserves an opportunity to tell his story", said Sen.
President Trump fired Comey last Tuesday. It says the president then told Russia's foreign minister and ambassador that he "faced great pressure because of Russian Federation". His testimony provides fuller details about Trump's termination of the top law enforcement official investigating whether his campaign colluded with the Russian government to influence the outcome of the 2016 election.
Trump, accompanied by wife Melania, walk across the South Lawn of the White House in Washington on Friday.
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Comey is known to produce memos documenting especially sensitive or unsettling encounters, such as after the February meeting.
Michael Allen, a former senior director on the National Security Council in the George W. Bush White House, said that transcripts of meetings with foreign leaders usually "are treated like the crown jewels". That was two days after Rosenstein named Mueller as a special counsel to investigate possible coordination between Russian Federation and the Trump campaign to influence the 2016 presidential election. He said in a statement that Comey had put unnecessary pressure on the president's ability to conduct diplomacy with Russian Federation on matters such as Syria, Ukraine and the Islamic State group.
A spokeswoman for House Speaker Paul Ryan said he would not discuss information provided in classified briefings and said the House Oversight committee had already asked for documents related to Comey's firing.
The announcement, the latest in the shock-a-day Washington saga, was made by deputy Attorney General Rod Rosenstein.
In closed-door meetings with lawmakers on Thursday and Friday, Rosenstein said he wrote the memo after Trump told him one day before the May 9 firing that he wanted to dismiss Comey.
Friday's report quotes Trump calling ousted Federal Bureau of Investigation director Comey "crazy" and "a real nut job".
Contacted by the Times, White House press secretary Sean Spice did not deny Trump had made the statements, saying Comey's "grandstanding and politicizing" of the Russian Federation probe had put "unnecessary pressure on our ability to engage and negotiate with Russian Federation".
The appointment of former FBI Director Robert Mueller as special counsel has drawn generally favorable comments from Democrats and from some Republicans as well.
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