Asked on NBC's "Meet the Press" whether the president had confidence in Flynn, senior policy adviser Stephen Miller said he did not know.
"It's not for me to tell you what's in the president's mind," Miller told moderator Chuck Todd. He added that his colleagues at the White House "did not give me anything to say" about Flynn.
When ABC News anchor George Stephanopoulos asked Miller about Flynn's interactions with Sergey Kislyak, Russia's ambassador to the United States, Miller said, "I don't have any news to make . . . today on this point."
The Washington Post revealed last week that Flynn and Kislyak had discussed U.S. sanctions against Russia in the month before Trump's inauguration.
The Post's finding, confirmed by nine current and former U.S. officials, contrasted with the assurances made publicly by Vice President Pence and other top administration officials that Flynn never talked about sanctions with Russian officials.
Based on Flynn's private assurances, Pence, White House Chief of Staff Reince Priebus and White House press secretary Sean Spicer stated publicly that Flynn never discussed sanctions with Kislyak.
Pence spoke to Flynn twice on Friday - once face to face and by telephone, according to an administration official who declined to characterize the contents of those discussions.
"Flynn is running out of friends, no question," a different administration official said. "The broad consensus in the White House is that he lied. The vice president feels like he lied. In a position that needs to be no drama, it's nonstop drama. I would be very surprised if he lasts much longer."
New Jersey Gov. Chris Christie, R, an informal adviser to Trump, called on Flynn to "clear up" what happened with Trump and Pence, but he stopped short of accusing him of wrongdoing.
"I think that's the obligation of General Flynn, his national security adviser, to have those type of candid conversations with the president and the vice president," Christie said on CNN. "And then they will act as they see fit, given all the circumstances."
Over the weekend at Trump's Mar-a-Lago Club in Palm Beach, Florida, the president privately voiced frustration with Flynn and the political baggage he is hanging on the White House, according to two people familiar with his comments.
Spicer denied that Trump criticized Flynn to anyone at the club and called assertions to the contrary "fake news."
People close to Flynn said he feels confident in his position despite the swirling controversy. He flew to Florida this weekend with the president along with other National Security Council officials to engage with his Japanese counterparts during Japanese Prime Minister Shinzo Abe's visit.
Furthermore, people in Trump's orbit cautioned that it would not be in the president's nature to fire Flynn because doing so would amount to an admission of guilt and misjudgment in the face of media scrutiny, as well as demonstrate chaos in the early weeks of his presidency.
The doubts about the national security adviser come as Trump faces his first significant provocation from a U.S. adversary overseas. North Korea fired a ballistic missile over the weekend, a move suspected by some experts as designed to serve as a test of components of an intercontinental ballistic missile capable of reaching the United States.
Trump responded on Saturday night in a joint appearance with Abe at Mar-a-Lago, where he reassured his Japanese counterpart that the United States fully supported Japan.
Flynn, a retired lieutenant general and a decorated intelligence officer, met Trump in late 2015 to offer advice about his campaign and signed on with Trump the following year. He won Trump's approval during the general election with his willingness to travel regularly and deliver fiery stump speeches trashing Trump's Democratic opponent, Hillary Clinton.
Democratic leaders have called for investigations into the Flynn's contact with Russian officials and for Trump to suspend and revoke Flynn's security clearance.
"President Trump's kowtowing to Vladimir Putin is endangering our national security and emboldening a dangerous tyrant," House Minority Leader Nancy Pelosi, D-Calif., said Saturday.
Rep. Elijah Cummings, Md., the top Democrat on the House Committee on Oversight and Government Reform, said today on ABC News that suspending Flynn's clearance would be "an appropriate action."
Trump has not yet issued a comment about Flynn, either on Twitter or in one of his brief appearances before journalists over the weekend. Aboard Air Force One on Friday, reporters asked Trump about The Post's report on Flynn's discussion of sanctions and the president claimed he did not know about it, even though it had by then become a major story across cable news.
"I don't know about that. I haven't seen it," Trump said during a flight to Florida from Washington. "What report is that? I haven't seen that. I'll look into that."