Donald Trump has broken his silence over the resignation of his national security adviser, saying the "real story" is the "illegal leaks" coming out of Washington.

Retired Lieutenant General Michael Flynn resigned yesterday, ending days of speculation about his fate following reports he'd misled Vice President Mike Pence and other officials about his contacts with Russia.

General Flynn conceded that discussions of sanctions may have come up during several calls with the Russian ambassador during the transition period leading up to Trump's January 20 inauguration.

"The real story here is why are there so many illegal leaks coming out of Washington? Will these leaks be happening as I deal on N.Korea etc?" President Trump tweeted.

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North Korea tested a ballistic missile over the weekend while Trump was at his Florida resort hosting Japanese Prime Minister Shinzo Abe.

Hillary Clinton has taken a wry swipe on Twitter at General Flynn following his resignation.

Clinton retweeted a post from longtime confidante Phillipe Reines, where he suggested General Flynn and his son, Michael Flynn Jr, get jobs at Domino's.

Flynn Jr circulated a fake news story tying the Clinton campaign to the so-called Pizzagate conspiracy theory, alleging in December that she had used the Comet Ping Pong pizzeria in Washington, DC to run a child sex-trafficking operation.

Flynn Jr was the first to be sacked from the Trump transition team before the presidential inauguration.

General Flynn was also one of Clinton's biggest critics regarding her email server and was seen at Trump rallies leading chants of "lock her up."

"Philippe's got his own way of saying things, but he has a point about the real consequences of fake news," Clinton said in her tweet.

Reines had written, "Dear Mike Flynn & Mike Flynn Jr., What goes around COMETS around. And given your pizza obsession ...", with a link to Domino's Pizza's job site.

Kellyanne Conway, senior adviser to President Trump, is said to be out of the loop. Photo / AP
Kellyanne Conway, senior adviser to President Trump, is said to be out of the loop. Photo / AP

Trump counsellor Kellyanne Conway, who only yesterday claimed that General Flynn had the "full confidence" of the president, revealed that Trump was not set to fire the national security adviser if he didn't resign.

Conway said during a 4pm interview that General Flynn was safe, but an hour later White House press secretary Sean Spicer said Trump was "evaluating" the situation. By 11pm, General Flynn had handed in his resignation.

Asked on the Today show who was right, Conway said "both were true," referring to her statement and Spicer's.

"The president is loyal. He's a very loyal person. And by night's end Mike Flynn had decided it was best to resign. He knew he had become a lightning rod and he made that decision."

Morning Joe host Joe Scarborough said that Conway, despite having walk-in privileges in the Oval Office, was among the last to know.

"She goes out and lies and you find out about those lies a couple hours later," Scarborough said.

"Or if she's not lying ... she is - actually what I've heard, she is so out of the loop. She's in none of the meetings and she just goes out without talking without having the facts."

General Flynn now has the dubious honour of being sacked by one US president for insubordination and now delivering his resignation to another.

Trump named retired Lt. Gen. Keith Kellogg as the acting national security adviser and a senior administration official said he was one of three candidates the president was considering to replace Gen. Flynn on a permanent basis.