US President Donald Trump has traded extraordinary insults with Democratic contender Michael Bloomberg on social media.

Trump called billionaire Bloomberg a "loser" to which the former New York mayor responded by calling the President "a carnival barking clown".

The exchange is the latest vicious resurgence of the bitter rivalry between the two New Yorkers. Bloomberg served three terms as New York City mayor and has variously been a Democrat, a Republican and an independent.

Democratic presidential candidate Michael Bloomberg made a point of his business record, compared with Donald Trump. AP Photo / Carlos Osorio
Democratic presidential candidate Michael Bloomberg made a point of his business record, compared with Donald Trump. AP Photo / Carlos Osorio

The media company mogul twice flirted with running for president as an independent candidate.

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Bloomberg is battling for the Democratic ticket with Pete Buttigieg, Bernie Sanders and Elizabeth Warren and others in a race which has blown out nationwide after caucuses in Iowa and New Hampshire failed to decide a leading contender.

Meanwhile, Trump also lashed out against former White House chief of staff John Kelly for being disloyal after the ex-adviser came to the defence of a former national security aide who offered key testimony in the impeachment inquiry.

The president's comments targeting Kelly came after Kelly defended Lt Col Alexander Vindman, who was among administration officials who raised concerns about Trump's July phone call with Ukraine's president.

That call spurred the president's impeachment trial, which ended in acquittal last week.

"Like so many X's, he misses the action & just can't keep his mouth shut,. which he actually has a military and legal obligation to do," Trump tweeted about Kelly.

"His incredible wife, Karen, who I have a lot of respect for, once pulled me aside & said strongly that 'John respects you greatly. When we are no longer here, he will only speak well of you.' Wrong!"

Kelly, speaking at a public forum on Wednesday in Morristown, New Jersey, said that Vindman did exactly as he was trained in raising concerns to his superiors after hearing "questionable" comments from Trump, according to a report by The Atlantic magazine.

Vindman was ousted last week from his position as a Ukraine specialist detailed to the White House National Security Council.

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"He did exactly what we teach them to do from cradle to grave," said Kelly, a retired Marine general who served as Trump's chief of staff from the summer of 2017 until early last year.

In this June 27, 2018 file photo, White House Chief of Staff John Kelly, right, leans in to talk with President Donald Trump. AP Photo / Pablo Martinez Monsivais
In this June 27, 2018 file photo, White House Chief of Staff John Kelly, right, leans in to talk with President Donald Trump. AP Photo / Pablo Martinez Monsivais

"He went and told his boss what he just heard."

Vindman was a key witness in Democrats' impeachment inquiry of Trump.

The Army officer was ousted from his job on the White House National Security Council last Friday, just two days after the Senate acquitted Trump on abuse of power and obstruction of justice charges. He is to be reassigned by the Pentagon. His twin brother, Lt Col Yevgeny Vindman, who worked as an ethics lawyer at the NSC, also was ousted from his job and was re-assigned to the Army General Counsel's Office.

Kelly came to Vindman's defence after Trump suggested this week that the Pentagon should review Vindman's conduct in the Ukraine episode and potentially consider disciplinary action against him.

Trump has insisted that his call to Zelenskiy was "perfect".

During the conversation, Trump asked Zelenskiy to do him "a favour" and look into former Vice President Joe Biden and his son's business dealings in Ukraine.

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Vindman testified that he raised his concerns inside the White House after concluding that Trump was inappropriately conditioning nearly $400 million in military aid to the country on getting Zelenskiy's help digging up dirt on the Republican president's political rival.

Kelly said at the forum that Vindman's decision to raise his concerns was valid.

"Through the Obama administration up until that phone call, the policy of the US was militarily to support Ukraine in their defensive fight against … the Russians," Kelly said. "And so, when the president said that continued support would be based on X, that essentially changed. And that's what that guy [Vindman] was most interested in."

Trump initially tapped Kelly after the 2016 election to serve as his secretary of Homeland Security, before Trump asked him to become his chief of staff. Kelly suggested at the forum he had some hesitation about joining the administration but ultimately decided to at the urging of his wife.

"I frankly think he needs you and people like you," Kelly recalled his wife telling him.

White House press secretary Stephanie Grisham said Thursday that she was "disappointed" by Kelly's comments. She compared him to former national security adviser John Bolton, another top aide who was critical of Trump's efforts to pressure Zelesnkiy.

"I thought it was a little disingenuous," Grisham said in an interview on Fox New Channel's Fox & Friends "It's interesting that he's starting to poke his head out a little bit more, just like John Bolton, as we're getting close to an election."

Bolton, according to excerpts of a manuscript leaked to the media during the Senate impeachment trial, says Trump told him he was conditioning the release of military aid to Ukraine on whether its government would help investigate the Bidens.

- AP