The have also requested Acting FBI Director Andrew McCabe any notes or memos prepared by Mr Comey "regarding any communications he may have had with any senior White House or Department of Justice officials."
According to the New York Times, Mr Comey had a habit of drafting these memos after any conversations with the president. Since his departure, the documents are now the property of the federal government, not Mr Comey's personal communications.
Mr Comey had responded to the committee's initial request to hold a closed session after his 9 May firing by saying he would testify but would prefer to do so publicly.
Normally, senior government officials at Mr Comey's level are given an opportunity to resign from their high-level posts as a sign of respect for their decades of public service. Mr Trump minced no words in his final letter to Mr Comey, however, saying that the FBI Director had eroded public trust and was no longer effective in his position.
The purpose of a closed session is likely so Mr Comey may share classified information regarding the ongoing investigation into alleged ties between Russia and Mr Trump's campaign team as well as Russia's possible interference into the 2016 US election.
The New York Times reported that Mr Trump had, during one of their conversations, asked Mr Comey to "let it go" when it came to the investigation into alleged ties between Russia and former National Security Advisor Mike Flynn.
The House is running a parallel investigation and has made a similar request for Mr Comey's memos. It is important to note that the Flynn investigation is a separate matter from the investigation into Mr Trump's campaign team, though both involve alleged ties to Russian officials.
There is no word yet whether Mr McCabe will also be asked to appear before the committee to discuss the investigation.
Mr Trump met with Russian Foreign Minister Sergei Lavrov and US Ambassador to Russia Sergei Kislyak, at the White House, just one day after he fired Mr Comey. The Washington Post later reported that Mr Trump divulged "highly classified" information from a US ally to the Russian officials.
Donald Trump's first 100 days: in cartoons
Donald Trump's first 100 days: in cartoons
Donald Trump's first 100 days in office were marred by a string of scandals, many of which caught the eye of the Independent's cartoonists
Trump's first 100 days have seen him aggressively ramp up tensions with his nuclear rivals in North Korea
Mr Trump has warned of a "major, major conflict" with the pariah nation lead by Kim Jong Un
Mr Trump dropped the "mother of all bombs" on alleged ISIS-linked militants in Afghanistan, amid an escalation of US military intervention around the globe
Mr Trump has been accused of falling short of the standards set by his predecessors in the Oval Office, including Franklin D Roosevelt
The tycoon's ascension to the White House came at a time when the balance of power is shifting away from Western nations like those in the G7 group
Western politicians, including the British Conservative party, have been accused of falling in line behind Mr Trump's proposals
Brexit is seen to have weakened Britain, reducing still further any political will to resist American leadership
Mr Trump's leadership has been marked by sudden and unexpected shifts in global policy
Trump's controversial missile strike on Syria, which killed several citizens, was seen by some analysts as an attempt to distract from his policy elsewhere
The President has also spent a large majority of his weekends golfing, rather than attending to matters of state
Though free of gaffes, a visit from Chinese president Xi Jinping spotlighted trade tensions between the two states
One major and unexpected setback came when Mr Trump's Healthcare Bill was struck down by members of his own party
Mr Trump has been a figure of fun in the media, with his approval at record lows
A string of revelations about Mr Trump's financial indiscretions did not mar his surge to the White House
Outgoing President Barack Obama was accused of wiretapping Trump Tower by his successor in America's highest office
The alleged involvement of Russian intelligence operatives in securing Mr Trump the presidency prompted harsh criticism
The explosive resignation of Security Adviser Michael Flynn, who lied about his links to the Russian ambassador, was just one scandal to hit the President
Many scandals, such as the accusation Barack Obama was implicated in phone-hacking, first broke on Mr Trump's Twitter feed
Donald Trump's election provoked mass protests in the UK, with millions signing a petition to ban him from the country
Donald Trump cited a non-existent terror attack in Sweden during a campaign rally
Donald Trump stands accused of stoking regional tensions in Eastern Asia
North Korea has launched a number of failed nuclear tests since Mr Trump took power
Theresa May formally rejected the petition calling for Mr Trump to be banned from the UK
When Mr Trump's initial so-called Muslim ban was struck down by a federal justice, the President mocked the 69-year-old as a "ridiculous", "so-called judge"
A week after his inauguration, Theresa May met with Mr Trump at the White House
Donald Trump's first days in office were marked by a hasty attempt to follow through on many of his campaign promises, including the so-called Muslim ban
Donald Trump's decision to ban citizens of many majority-Muslim countries from the US sparked mass protests
Revelations about Donald Trump's sexual improprieties were not enough to keep him from being elected President
British PM Theresa May was criticised by many in the press for cosying up to the new President
One of Mr Trump's top aides, Kelly Anne Conway, was mocked for describing mistruths as "alternative facts"
British PM Theresa May was quick to demonstrate that her political aims did not hugely differ from Mr Trump's
Donald Trump's inauguration, on 20 January 2017, sparked protests both at home and abroad
The report, which cited a confidential source within the administration, set off a firestorm.
“This is code-word information,” one US official told the newspaper, a reference to one of the highest classification levels used by the American intelligence agencies, adding that Mr Trump had revealed more to Russia than the US does to some allies.
National Security Advisor HR McMaster said that “at no time were any intelligence sources or methods discussed and no military operations were disclosed that were not already known publicly.”
Mr McMaster said he was in the room and "it didn't happen."
However, the Washington Post report did not include any information about "sources and methods," causing some to speculate why Mr McMaster would deny something that was not reported.
Later, he said that the conversation was "wholly appropriate" and that what was shared could have been learned from open sources.
What worried many in Washington was that Mr Trump "wasn't even aware of where this information came from" at the time of the meeting with Russian officials. He had not been briefed on it according to the national security advisor.
In fact, Mr McMaster said the president made the decision to share the information "in the context of the conversation." In other words, Mr Trump decided spontaneously to share the sensitive information.
Russian President Vladimir Putin then responded, saying that no classified information had been shared with his officials. This begs the question, how would they know if a piece of information was classified or not and would they admit it if they learned classified information.
Congressman Al Green became the first person to call for Mr Trump's impeachment on the House floor. Maxine Waters, the representative from California, has been saying there were grounds for possible impeachment in the media for months but never took to the floor for a formal statement.
Republican Chair of the House Oversight Committee Jason Chaffetz said the House needs to see the memos Mr Comey wrote in order to determine if Mr Trump did in fact obstruct justice by calling for the end of the Flynn investigation. House Speaker Paul Ryan supported the request, however neither have asked for a hearing with Mr Comey or McCabe as yet.
Another New York Times report revealed that the US ally from whom the information Mr Trump shared originated was Israel.
Prime Minister Benjamin Netanyahu has not responded to the report but depending on the information shared, it could put lives of US and ally intelligence officers in the Middle East at risk according to some experts.
Mr Trump also had a call with regional ally Jordan the day after the report.
Thus far, the White House and Mr Trump's Twitter account have continued to take the stance that Mr Trump did not share any classified information.
He is scheduled for his foreign visit as president on 18 May, travelling to Saudi Arabia, Israel, and the Vatican including stops in Italy for the group of seven meeting.
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