Michael Flynn quit on February 13 over claims he discussed US sanctions with Russia before President Donald Trump took office.
On February 14, a White House spokesman said President Trump knew weeks ago there were problems with the Russia phone calls.
However, calls for an independent investigation have encountered a cold response from some senior Republicans.
The development came as the New York Times reported that phone records and intercepted calls show members of Donald Trump’s presidential campaign, as well as other Trump associates, “had repeated contacts with senior Russian intelligence officials in the year before the election”.
However, officials spoken to by the newspaper said they had not yet seen evidence that the Trump campaign colluded with Russia on the hacking of the DNC or to influence the election.
As well as an FBI investigation, both the Senate and House intelligence committees are already examining Russian involvement in the election. It is not yet clear whether the latest claims will be included in their scope.
Michael Flynn stood down over allegations he discussed US sanctions with a Russian envoy in December, before Donald Trump took office.
The conversations took place about the time that then-President Barack Obama was imposing retaliatory measures on Russia following reports it attempted to sway the US election in Donald Trump’s favor.
Michael Flynn could have broken a law – known as the Logan Act – by conducting US diplomacy as a private citizen, before he was appointed as national security adviser.
The retired army lieutenant-general initially denied having discussed sanctions with Ambassador Sergei Kislyak. VP Mike Pence publicly denied the allegations on his behalf.
The White House admitted it had been warned about the contacts on January 26 but President Trump initially concluded Michael Flynn had not broken any law.
White House lawyers then conducted a review and questioned Michael Flynn before reaching the same conclusion as Donald Trump, White House spokesman Sean Spicer said, but the trust had gone.
White House Counsellor Kellyanne Conway said on February 14: “In the end, it was misleading the vice-president that made the situation unsustainable.”
Michael Flynn was also reportedly questioned by FBI agents in his first days as national security adviser.
In an interview conducted with The Daily Caller on February 13, but published only on February 14, Michael Flynn said he “crossed no lines” in his conversation with the ambassador.
The former national security adviser said he discussed the expulsion of 35 Russian diplomats over alleged hacking ahead of the election, but “it wasn’t about sanctions”.
Michael Flynn said he was concerned that the apparently classified information had been leaked. He said: “In some of these cases, you’re talking about stuff that’s taken off of a classified system and given to a reporter.
“That’s a crime.”
However, in his resignation letter, Michael Flynn said “the fast pace of events” during the presidential transition meant that he had “inadvertently briefed the vice-president elect and others with incomplete information regarding my phone calls with the Russian ambassador”.
In his first public comments about the controversy, President Trump tweeted on February 14: “The real story here is why are there so many illegal leaks coming out of Washington? Will these leaks be happening as I deal on N Korea etc?”
US House Intelligence Committee Chairman Devin Nunes told reporters on February 14 he wanted to examine the leaks, and said the FBI should explain why Michale Flynn’s conversation had been recorded.
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