Michael Flynn quit on Monday over claims he discussed US sanctions with Russia before Donald Trump took office.
On Tuesday, a White House spokesman said Mr Trump knew weeks ago there were problems with the Russia phone calls.
But 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 Mr 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 Democratic National Committee 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.
Why Mr Flynn resigned
He stood down over allegations he discussed US sanctions with a Russian envoy in December, before Mr 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 Mr Trump’s favour.
Mr 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.