Mr Flynn has entered a plea deal and agreed to co-operate with an inquiry into alleged collusion with Russia.
The deal, for a lesser charge than he might have faced, prompted speculation that he has incriminating evidence.
The president wrote on Twitter on Saturday that he had “nothing to hide”.
Mr Flynn is cooperating with Special Counsel Robert Mueller, who is leading an investigation into alleged ties between the Trump campaign and Russia ahead of the 2016 election.
On Saturday, a day after Mr Flynn’s indictment, it emerged that a veteran FBI agent was dismissed from Mr Mueller’s team after the discovery that he had sent anti-Trump text messages.
Peter Strzok was removed from the investigation in summer, a spokesman for the special counsel’s office, told the New York Times.
Saturday should have been a momentous day for Mr Trump, after his sweeping tax reform bill finally scraped through the senate in the early hours of the morning with 51 votes to 49.
But any celebratory mood among administration officials would have been short-lived – dampened by a string of news reports on the Russia scandal.
In tweeting early on Saturday to deny that Mr Flynn had acted unlawfully as part of his transition team, Mr Trump appeared to admit that he knew the former general had lied to the FBI before he fired him, contradicting the president’s account at the time.
Analysts say if Mr Trump knew that Mr Flynn had lied to the FBI, at a time when he appeared to pressure then-FBI director James Comey to drop the agency’s investigation into the former general, it could amount to obstruction of justice by the president.
Matthew Miller, a former Obama administration Justice Department official, said in a tweet: “Oh my god, he just admitted to obstruction of justice. If Trump knew Flynn lied to the FBI when he asked Comey to let it go, then there is your case.”
Meanwhile, the New York Times reported that it had obtained internal emails sent by Mr Trump’s transition team that disputed the White House assertion that Mr Flynn acted alone in his contacts with Russian officials.
In one email quoted by the paper, a senior adviser appeared to say that Russia had “just thrown the U.S.A. election to him”, referring to Mr Trump.
A White House lawyer told the paper that the adviser, KT McFarland, had meant only that the Democrats were portraying it that way.
Under the terms of the plea deal with Mr Mueller, Mr Flynn admitted making false statements to the FBI, a significantly lesser charge than he might have faced for illegally dealing with Russian officials.
Analysts say the deal suggests that the former general has evidence implicating one or more senior members of the Trump administration.
Mr Flynn has admitted lying about his contact with the Russian ambassador Sergei Kislyak in December 2016 – after Mr Trump was elected but before he became president.
The charging documents against Mr Flynn state that he was directed to make contact with Russian officials by a “very senior member” of the Trump transition team.
Several US news organisations report the very senior official now under the spotlight is Jared Kushner – Mr Trump’s adviser and son-in-law.
US intelligence agencies say Russia’s President Vladimir Putin directed a state effort to influence the US election in favour of Mr Trump.
Mr Trump has repeatedly denied that his campaign or transition team colluded in Russian actions. Speaking to reporters on Saturday, he said: “What has been shown is no collusion, no collusion. There has been absolutely no collusion. So we’re very happy.”
Mr Flynn was questioned by the FBI shortly after Mr Trump took office in January about his December meetings with Mr Kislyak. He was forced to resign in February, 23 days into his job.
According to the FBI’s statement of offence signed by Mr Flynn, he discussed Russia’s response to US sanctions as well as a UN Security Council resolution on Israel, at the direction of the Trump team.
Under the Logan Act it is illegal for a private US citizen, as Mr Flynn was during the transition period, to conduct foreign affairs without the permission or involvement of the US government. (Courtesy BBC)