Reps. John Conyers of MI and Elijah Cummings of Maryland called Flynn "unfit" to be national security adviser and said he should have been dismissed weeks ago.
Spicer said Trump will evaluate potential successors to Flynn immediately.
Mr Trump spoke for more than an hour, airing his grievances about the media, in a press conference originally meant to formally announce his new Labour Secretary nominee, Alexander Acosta.
Flynn reportedly apologised on Monday to Pence, saying that he may have discussed the Obama administration's sanctions with Kislyak before Trump was sworn in. Later, however, the Federal Bureau of Investigation discovered that the contents of Flynn's call were actually "highly significant" and that the former Army lieutenant general did indeed discuss sanctions with the diplomat-a revelation that made Pence "feel lied to", according to business site Axios. "It's a criminal action, criminal act, and it's been going on for a long time before me, but now it's really going on".
Grave questions have been raised about the fitness of General Flynn to serve as National Security Adviser and to continue having access to classified information. Although Flynn has taken substantial criticism for potentially discussing sanctions, Spicer said White House counsel had investigated the matter and concluded there was nothing illegal about it. That led Flynn to resign Monday at the request of Trump.
"The reason they lost faith or trust in General Flynn only last night when they knew for weeks that he had been lying was that it became public", Schiff told MSNBC.
Ivanka and Melania Trump will share 'the First Family Office'
The 35-year-old made her debut solo appearance as First Lady when she met the Japanese Prime Minister's wife. Melania Trump has signaled her intention to use her time in the spotlight to build her "brand".
"The truth and consequences of the Russian Federation connection: the American people deserve to know the full extent of Russia's financial, personal and political grip on President Trump and what that means for our national security", Pelosi said. You saw it. And the leaks are absolutely real. No person that I deal with does.
Republican John McCain, chairman of the Senate armed services committee, said Mr Flynn's resignation was a "troubling indication of the dysfunction of the current national security apparatus" and raises questions about Mr Trump's intentions towards Russian Federation.
Several house Democrats called on oversight committee chairman Jason Chaffetz, a Republican from Utah, to launch an investigation into Mr Flynn's ties to Russian Federation. And what hold might Russian Federation have over officials who now know from the example of Mr Flynn that exposure can cost them their job?
Lawmakers involved said they want to move quickly, but thoroughly, on the Russian Federation investigation. Sen. "It's nothing to do with us".
Congressional leaders said they will investigate growing questions over contacts between Russian Federation and top aides to U.S. President Donald Trump in the weeks and months before he took office.
Congressional democrats John Conyers and Elijah Cummings have demanded a classified briefing to Congress on Michael Flynn by the justice department and Federal Bureau of Investigation.