U.S. President Donald Trump knew for weeks that national security adviser Michael Flynn had misled the White House about his contacts with Russia but did not immediately force him out, an administration spokesman said on Tuesday.

Trump was informed in late January that Flynn had not told Vice President Mike Pence the whole truth about conversations he had before Trump took office with Russia's ambassador to the United States, White House spokesman Sean Spicer said.

Pence learnt of the "incomplete information" that he received from Flynn when news reports surfaced late last week, spokesman Mark Lotter said on Tuesday.

Flynn quit on Monday after Trump asked for his resignation, and the president hopes to pick a new national security adviser by the end of the week, Spicer said.

The departure was another disruption for an administration already repeatedly distracted by miscues and internal dramas since the Republican businessman assumed the presidency on Jan. 20.

U.S. lawmakers, including some leading Republicans, called for a deeper inquiry into not just Flynn's actions but broader White House ties to Russia. Trump has long said that he would like improved relations with Russian President Vladimir Putin.

Representative Adam Schiff, the top Democrat on the House of Representatives Intelligence Committee, said Trump only moved against Flynn because of news media attention, not concern about any wrongdoing.

"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.

A timeline of events outlined by Spicer and a U.S. official showed that Trump had known for weeks about Flynn misleading the vice president.

Trump, a former reality TV star whose catchphrase was "You're fired!" has often boasted of his eagerness to get rid of subordinates. He was not quick to fire Flynn, a strong advocate of a better relations with Russia and a hard line against Islamist militants.

The Justice Department warned the White House in late January that Flynn had misled Pence by denying to him that he had discussed U.S. sanctions on Russia with Ambassador Sergei Kislyak, a potentially illegal act, a U.S. official said.

Flynn did talk about sanctions with the diplomat, whose calls were recorded by U.S. intelligence officials, the official said. But Pence went on television in mid-January and denied that Flynn had discussed sanctions.

The Federal Bureau of Investigation interviewed Flynn in his early days as Trump's national security adviser regarding his conversations with the Russian ambassador, a White House official confirmed.

Spicer stressed that the administration believed there was no legal problem with Flynn's conversations with Kislyak, but rather an issue over the president's trust in his adviser.

The turning point, Spicer said, was a Washington Post story published on Thursday in which Flynn, through a spokesman, said for the first time he could not say with 100 percent certainty that he had not discussed sanctions with Kislyak.

Spicer said the Justice Department sought to notify the White House counsel on Jan. 26 about the discrepancies in Flynn's accounts.

"The White House counsel informed the president immediately. The president asked them to commit a review of whether there was a legal situation there," Spicer told reporters, saying it was a "trust issue."

Flynn's conversations with the ambassador took place around the time that then-President Barack Obama imposed sanctions on Russia, charging that Moscow had used cyber attacks to try to influence the 2016 presidential election in Trump's favour.

A U.S. official familiar with the transcripts of the calls with the ambassador said Flynn indicated that if Russia did not retaliate in kind for Obama's Dec. 29 order expelling 35 Russian suspected spies and sanctioning Russian spy agencies, that could smooth the way towards a broader discussion of improving U.S.-Russian relations once Trump took power.

LEGAL FALLOUT?

Flynn's discussions with the Russian diplomat could potentially have been in violation of a law known as the Logan Act, which bans private citizens from negotiating with foreign governments about disputes or controversies with the United States. There have been no modern prosecutions using the 1799 law.

"The Logan Act is a red herring. The better question is whether he made any false statements to the FBI at any point, which would be a much bigger deal," said University of Texas law professor Stephen Vladeck, adding the fallout would likely be "political" in nature.

Flynn could also face legal trouble if it emerges that he violated other federal laws in his communications with the Russians, said Andrew Kent, a professor at Fordham University School of Law in New York. The Espionage Act criminalises sharing information with foreign governments.

Democrats, who do not have control of Congress, clamoured for probes into Flynn, and asked how much Trump knew about his connections to Russia.

U.S. Senate Democratic leader Chuck Schumer called for an investigation of potential criminal violations surrounding the resignation of Flynn.

"What I am calling for is an independent investigation with executive authority to pursue potential criminal actions," Schumer told reporters, saying such a probe could not be led by newly installed U.S. Attorney General Jeff Sessions or White House lawyers.

Two leading Senate Republicans, Bob Corker and John Cornyn, said the Intelligence Committee should investigate Flynn's contacts with Russia.

But the highest-ranking Republican in Congress, House of Representatives Speaker Paul Ryan, sidestepped questions about whether lawmakers should look into Flynn's Russia ties, saying he would leave it to the Trump administration to explain the circumstances behind Flynn's departure.

A broader investigation of the White House and its ties to Russia is not possible without the cooperation either of the Justice Department or the Republican-led Congress.

Russia's aggression in Ukraine and Syria and Republican congressional opposition to removing sanctions on Russia make any White House attempt to embrace Putin problematic.

Senator John McCain, a leading Republican voice on foreign relations, said Flynn's resignation raised questions about the administration’s intentions towards Putin’s Russia.