"He was insane, a real nut job", Trump allegedly said to the Russian envoys.
Mr Trump has denied any collusion with Russian Federation, and called the investigation into his campaign the "single greatest witch hunt of a politician in American history".
Capping days of political drama in Washington, Mueller's appointment came as Trump fends off a stunning series of allegations including claims he shared U.S. secrets with Russian officials in the Oval Office.
White House press secretary Sean Spicer did not dispute the account of the conversation to The Times and, in a statement to NPR, argued that the Russian Federation investigation was harming US foreign policy. He says he hopes Comey's testimony will answer some of the questions that have arisen since Comey was suddenly dismissed last week by President Donald Trump.
He added, "The investigation would have always continued, and obviously, the termination of Comey would not have ended it".
Trump's dismissal of Comey was met with bipartisan derision.
At the same meeting, the The Washington Post reported earlier this week that Trump had given the Russians "highly classified information", which "jeopardized a critical source of intelligence" on ISIS that came from a key ally, which, according to later reports, was Israel.
The President maintains he was surprised by the response to Comey's firing.
Trump had said Thursday he was "very close" to naming a replacement and that former Connecticut Sen. "When I made that decision, I actually thought that it would be a bipartisan decision". In other words, it looks like this thing goes straight to the top.
The president also reportedly told the Russians, "I'm not under investigation". News reports that Comey had written memos about his conversations with Trump since January have fueled that aspect of the probe.
Deputy Attorney General Rod Rosenstein has told members of Congress he stands by a memo he wrote that preceded the president's firing of FBI Director James Comey.
Mr Trump met with the Russians on 10 May - the day after Mr Comey was sacked. "Regardless of the recommendation, I was going to fire Comey".
A Justice Department spokeswoman told the Post that she "can't confirm or deny the existence or non-existence of investigations or targets of investigations".
It came two days after Mr Rosenstein named Mr Mueller as a special counsel to investigate possible co-ordination between Russian Federation and the Trump campaign to influence the 2016 presidential election.
"I believe it hurts our country terribly, because it shows we're a divided, mixed-up, not-unified country", Trump said at a luncheon with a group of television news anchors.
Trump's meeting with Lavrov and Kislyak was controversial before news of talk about Comey ever came out. The meeting was also a personal request from Vladimir Putin.
Cummings called the report "astonishing - and extremely troubling".
A current White House official has been identified as a person of interest by law enforcement investigating possible collusion between Russian Federation and Donald Trump's presidential campaign, NBC News confirmed, citing two USA officials. Patrick Leahy: 'I'm willing to appoint a special counsel, Senator, whenever I determine that it's appropriate based upon the policies and procedures of the Justice Department'.
And Sen. Brian Schatz, a Hawaii Democrat, said, "Sorry for yelling guys".