J. Brien Comey said, adding tongue-in-cheek: "Incidentally, I told him I thought he and Trump would testify side by side in front of these congressional committees".
Regarding the emergence of a White House official as a person of interest in the FBI probe, Mr Spicer said: "As the President has stated before - a thorough investigation will confirm that there was no collusion between the campaign and any foreign entity".
At least one of the conversations - with NSA Director Rogers - was documented in a memorandum retained by the NSA.
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.
McConnell says a Senate Intelligence Committee investigation into the Russian effort to affect the election will also proceed.
Trump has denied any wrongdoing, and railed against the investigations into his campaign's alleged ties to Russian Federation repeatedly.
But, the Post noted, this was viewed by both current and former top intelligence officials "as an attempt by the president to tarnish the credibility of the agency leading the Russian Federation investigation".
The White House did not deny that Trump had been critical of Comey to Russian officials.
"The President has always emphasized the importance of making deals with Russian Federation as it relates to Syria, Ukraine, defeating ISIS and other key issues for the benefit and safety of the American people", the statement said.
The Washington Post reported Friday that a senior White House adviser who is close to Trump was a "significant person of interest" in the probe into possible coordination between the Trump campaign and Russian Federation during the presidentail election.
EPL: Tottenham collapse, give Chelsea more room to emerge champions
Speaking after the match, Spurs manager Mauricio Pochettino said: "We are feeling disappointed ". They have also played on extra match.
Sen. Dianne Feinstein, a member of the intelligence committee, said she also plans to press Comey regarding what was discussed with Trump about Flynn and whether he was asked by Trump to alter the FBI investigation.
Flynn reportedly told Trump's chief lawyer Donald McGahn on January 4 that he was under investigation for secretly working as a paid lobbyist for Turkey during the campaign.
Two days after firing Michael Flynn as his national security adviser in February, President Donald Trump told several aides and friends he should have kept him instead.
"A lot of people in the White House don't want anything to do with Flynn", one White House official said.
"We have multiple layers of investigations", Jenkins said.
Others say the motive is more about their bond - which, unlike some in Trump's world is real, White House officials say.
James Comey deserved to be fired for his actions around the Clinton email investigation during the presidential campaign.
Trump commented late Wednesday after the Justice Department announced the appointment of former Federal Bureau of Investigation director Robert Mueller to oversee the probe into Trump-Russian connection in the 2016 election.
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House Democrats who have been pressing for a special counsel to examine possible collusion between Russian Federation and the Trump campaign are welcoming word from the Justice Department that former FBI director Robert Mueller will lead the investigation.
West Virginia Sen. Joe Manchin, a Democrat on the Senate intelligence committee, said on CNN's "Erin Burnett OutFront" that he was as "shocked as anybody else" upon hearing the news and noted Coats and Rogers had appeared before the panel earlier this month.