Mr Flynn reportedly discussed sanctions with a Russian official in the weeks before Mr Trump took office.
He denied talking about this issue but later said he could not be certain.
Any discussion of sanctions could have violated laws against private citizens engaging in foreign policy.
Stephen Miller, President Donald Trump's top policy adviser, declined to say when asked in a number of interviews whether Mr Trump backed Mr Flynn.
Mr Miller said it was not his place to comment on the "sensitive matter" concerning Mr Flynn, who was an early supporter of Mr Trump but whose position in the administration is thought to be under scrutiny.
Mr Flynn spoke with Russia's ambassador, Sergei Kislyak, by phone in December.
Both Mr Flynn and US Vice-President Mike Pence denied that the two men discussed US sanctions imposed over Russia's actions in Ukraine and alleged hacking of the US Democratic Party.
But nine current and former officials later told the Washington Post that the issue had been discussed.
A spokesman subsequently told reporters that Mr Flynn "couldn't be certain" he had not discussed the sanctions.
Mr Trump, who spent the weekend at his club in Florida, Mar-a-Lago, has not commented on the controversy. Mr Flynn is understood to have also been at Mar-a-Lago over the weekend.
Mr Trump is said to be troubled by the situation and uncertain as to whether he will ask Mr Flynn to step down, the AP reported, citing administration officials.
Several other White House officials, as well as Mr Miller, declined over the weekend to comment on the situation.

The pair, dressed in Team GB tracksuits and wearing plastic medals, admitted to Sky News they "blagged" their way on to the float and joined the celebrations.
The float was carrying Britain's gold medal-winning women's hockey team and athletes from the modern pentathlon.
The BOA said: "It didn't spoil anyone's enjoyment of a wonderful event."
"We are aware of the matter and are disappointed anyone would want to detract from the athletes' celebration," it added.
Four hundred athletes took part in the Manchester celebrations with more 150,000 people lining the streets.
A second parade is to take place in Trafalgar Square in London from 13:00 BST after which the athletes will visit Buckingham Palace.
Greater Manchester Police said it did not provide security for the floats and had received no reports regarding the incident.
Manchester City Council is yet to comment.
Team GB set an Olympic record in Rio 2016 by winning 67 medals - two more than they managed at London 2012.
The Paralympians also beat their previous performance with 147 medals - 27 more than four years ago.
A top White House official declined in several interviews over the weekend to defend national security adviser Michael Flynn, amid controversy over his alleged contacts with Russia.
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Two imposters sneaked on to a float during the celebratory Rio 2016 parade in Manchester, the British Olympic Association (BOA) has confirmed.