And in an exclusive report, Reuters states Federal Bureau of Investigation and congressional investigators are looking at 18 phone calls and emails between Russian officials and Flynn and others in the Trump campaign.
Thursday afternoon, Deputy Attorney General Rod Rosenstein, the man who appointed Mueller, briefed senators behind closed doors.
President Trump told Russian officials last week that he had fired the "nut job" FBI Director James Comey to ease the pressure of the mounting investigation into his campaign's ties to Russia, according to a report from The New York Times.
"With all of the illegal acts that took place in the Clinton campaign & Obama Administration, there was never a special counsel appointed!"
Citing unnamed sources, the Washington Post reported that Trump had shared intelligence with Lavrov regarding an Islamic State group terror threat related to the use of laptop computers on airplanes.
Democratic Senator Amy Klobuchar responded, "This is a truth hunt".More news: Rod Rosenstein: Jeff Sessions, Donald Trump wanted James Comey gone
US stocks rose as upbeat economic data emboldened investors to return to the market on Thursday, a day after Wall Street saw its worst selloff in eight months on worries that the political turmoil could sideline Trump initiatives such as tax cuts that investors see as favouring economic growth. "I faced great pressure because of Russian Federation".
Some congressional Republicans have also suggested that Mueller's appointment would lead to changes in Congress' investigation.
Asked point-blank if he'd done anything that might merit prosecution or even impeachment, Trump said no - and then added of the lingering allegations and questions: "I think it's totally ridiculous".
Mr Rosenstein's disclosure seems to confirm Mr Trump's version of the story - that he had made up his mind to fire Mr Comey before the Justice Department wrote their memos about him.
In March, for example, the White House disclosed that Trump's son-in-law and White House senior adviser, Jared Kushner, met executives of Russian state development bank Vnesheconombank, or VEB, in December.
Hours earlier, on Twitter, Trump more colorfully called Rosenstein's appointment of Mueller as special counsel "the single greatest witch hunt of a politician in American history!" He was sacked as national security adviser in February after it emerged he had misled Vice President Mike Pence about conversations with the Russian ambassador to Washington in December.More news: Trump told Russians pressure off after firing 'nutjob' Comey
"The Intelligence Committee in the Senate has to continue its work, and it should continue full throttle ahead", Minority Leader Chuck Schumer said after the briefing.
Russian Federation has denied the allegations.
The FBI's investigation seeks to determine whether and to what extent Trump associates were in contact with Kremlin operatives, what business dealings they might have had in Russian Federation, and whether they in any way facilitated the hacking and publishing of emails from the Democratic National Committee and Hillary Clinton's campaign chairman, John Podesta, during the presidential campaign.
Rosenstein was due to brief USA senators later on Thursday.
Although Putin used the Russian word for audio recording at the press conference, his foreign policy aide Yuri Ushakov said that "audio is not made" at such meetings.More news: Trump tells Russians Comey was a 'nut job'
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