President Donald Trump has used a series of explosive tweets to blame the media and "illegally leaked" intelligence information for bringing down his national security adviser Michael Flynn.

Mr Trump's comments came one day after the White House said Mr Trump had asked Mr Flynn to resign because he misled Vice-President Mike Pence about his contacts with Russia.

Key points: Donald Trump says "it is a really sad thing [Michael Flynn] was treated so badly"

Donald Trump says "it is a really sad thing [Michael Flynn] was treated so badly" Mr Flynn was forced to resign as national security adviser over contact with Russia

Mr Flynn was forced to resign as national security adviser over contact with Russia Mr Trump reportedly thought Mr Flynn would survive the controversy until a series of explosive articles made the situation untenable

Mr Flynn's ousting has sparked a new swirl of controversy over Mr Trump's potential ties to Moscow.

Mr Flynn resigned earlier this week at the behest of Mr Trump, the White House later said, after reports that he had discussed sanctions with Russia's ambassador to the US before the inauguration, despite previously denying those conversations to Mr Pence and other top officials.

But in Mr Trump's first public comments on Mr Flynn, he appeared to side with his former aide, saying it was "really a sad thing that he was treated so badly".

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Mr Trump is said to favour Vice Admiral Robert Harward, a former Navy SEAL, as his next national security adviser, according to a White House official.

Vice Admiral Harward met with top White House officials last week and has the backing of Defence Secretary Jim Mattis.

Mr Flynn's resignation was a blow to a White House struggling to find its footing in Mr Trump's first weeks in office.

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The questions about Russia only deepened yesterday when The New York Times reported that US agencies had intercepted phone calls last year between Russian intelligence officials and members of Mr Trump's 2016 campaign team.

Current and former US officials who spoke to The Times anonymously said they found no evidence that the Trump campaign was working with the Russians on hacking or other efforts to influence the election.

Mr Trump did not directly address the veracity of the report during a news conference with Israeli Prime Minister Benjamin Netanyahu, but lashed out at what he called the "criminal act" of leaking information.

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Mr Trump ignored shouted questions about whether his advisers were in touch with Russian officials. His spokesman denied such contacts as recently as Tuesday afternoon (local time).

Democrats called for an independent investigation into Mr Trump's Russia ties and urged Republicans to join them.

"This is a moment for Republicans to put country ahead of party," Connecticut senator Chris Murphy said.

"There's only one or two times like this in your political career where you face a moment like this where what's good for your country may not be good for your party."

GOP lawmakers, led by Majority Leader Mitch McConnell, resisted, saying that the existing congressional committees will continue their investigations into Russian interference in the presidential election.

Michael Flynn (centre) resigned after conceding he gave "incomplete information". ( AP: Susan Walsh )

Trump thought Flynn would survive

Mr Flynn maintained for weeks that he had not discussed US sanctions in his conversations with Russia's ambassador. He later conceded that the topic may have come up.

Mr Trump initially thought Mr Flynn could survive the controversy, according to a person with direct knowledge of the President's views, but a pair of explosive stories in The Washington Post in recent days made the situation untenable.

As early as last week, he and aides began making contingency plans for Mr Flynn's dismissal, a senior administration official said.

While Mr Trump was said to be upset with Mr Flynn, he also expressed anger with other aides for "losing control" of the story and making his young administration look bad.

Mr Pence, who had vouched for Mr Flynn in a televised interview, is said to have been angry and deeply frustrated.

Mr Pence's spokesman Marc Lotter said Mr Pence became aware that he had received "incomplete information" from Mr Flynn only after the first Washington Post report last Thursday night.

At about the same time, Mr Pence learned that the Justice Department had warned the White House last month regarding Mr Flynn's conversations with Russian Ambassador Sergey Kislyak.

Mr Flynn, in an interview with The Daily Caller News Foundation, said "there were no lines crossed" in his conversations with Mr Kislyak.

The officials and others with knowledge of the situation were not authorised to discuss the matter publicly and requested anonymity.

Ahead of the January 20 inauguration, Mr Pence and other officials insisted publicly that Mr Flynn had not discussed sanctions in his talks with the Russian ambassador.

On January 26, Acting Attorney-General Sally Yates contacted White House counsel Don McGahn to raise concerns about discrepancies between the public accounting and what intelligence officials knew to be true about the contacts based on routine recordings of communications with foreign officials who are in the US.

The Justice Department warned the White House that the inconsistencies would leave the President's top national security aide vulnerable to blackmail from Russia, according to a person with knowledge of the discussion.

The President was informed of the warnings the same day, Press Secretary Sean Spicer said.

Mr Flynn was interviewed by the FBI around the same time, according to a US official who was briefed on the investigation.

Sorry, this video has expired Flynn resignation based on trust issue, not legal: Spicer

AP