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 with Russia's ambassador to the United States before Trump took office, White House spokesman Sean Spicer said.

Flynn quit on Monday after Trump asked for his resignation, Spicer said. "The issue pure and simple came down to a matter of trust," Spicer told reporters.

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.

The New York Times reported late on Tuesday that members of Trump's campaign and other associates had contact with senior Russian intelligence officials in the year before the Nov. 8 presidential election, although U.S. officials told the newspaper they had not uncovered any evidence that Trump's associates colluded to disrupt the election.

The Kremlin denounced the report early Wednesday in Moscow.

"Let's not believe anonymous information," Kremlin spokesman Dmitry Peskov told a conference call with reporters, noting that the newspaper's sources were unnamed. "It's a newspaper report which is not based on any facts."

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 media attention to the issue, and not because of concern at any wrongdoing by the former lieutenant-general.

"The reason they lost faith or trust in Gen. Flynn only last night when they knew for weeks that he had been lying was that it became public," Schiff told MSNBC.

Democratic Senator Chris Coons asked why Flynn was allowed to remain in his post for so long after the White House was warned of the potential for blackmail.

Representative Adam Schiff says Flynn's resignation was because the public learned about his conversations with Russia. (Alex Wong/Getty Images)

"This isn't just about what happened with Gen. Flynn," Coons told MSNBC. "What did President Trump know? What did the president know and when did he know it?" Coons said, echoing a question made famous by the Watergate scandal, which forced President Richard Nixon to resign in 1974.

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. But he was not quick to fire Flynn, a strong advocate of better relations with Russia and a hard line against Islamist militants.

An issue of trust

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.

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.

U.S. national security adviser Flynn quits after giving 'incomplete information' to VP Pence about discussions with Russian ambassador 2:09

He 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. That was immediately determined there wasn't. That was what the president believed at the time from what he had been told and he was proved to be correct," Spicer told reporters.

"We got to a point not based on a legal issue, but based on a trust issue," he said.

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 cyberattacks to try to influence the 2016 presidential election in Trump's favour.

Flynn's discussions with the Russian diplomat could potentially violate a law, known as the Logan Act, banning private citizens from negotiating with foreign governments about disputes or controversies with the United States. However, nobody has been prosecuted in modern times under the law, which dates from 1799.

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

Calls for investigation

House Speaker Paul Ryan deferred to the White House to explain the circumstances around Flynn's departure on Monday. (J. Scott Applewhite/Associated Press)

U.S. Senate Democratic leader Chuck Schumer called for an investigation of potential criminal violations surrounding the resignation of Flynn and said senior Trump administration officials should face tough questions.

Schumer said any probe could not be led by U.S. Attorney General Jeff Sessions or White House lawyers.

Two leading Republicans in the Senate, 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, adding that 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 co-operation 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 toward Putin's Russia.