Donald Trump has refused to answer questions about his own health after his contact with three people who have quarantined themselves amid fears they might have coronavirus.

Mr Trump abruptly left a White House press briefing on Monday (local time) without taking questions about his own health.

Vice-President Mike Pence said shortly after he did not know if the President had been tested for the coronavirus, but said he would try to find out.

One of the three is Florida House representative Matt Gaetz, who flew to Maryland on Air Force One with Mr Trump on Monday.

Mr Gaetz apparently learned shortly after the plane was airborne that he had been in contact with a person at the Conservative Political Action Conference in Maryland in late February who since has been diagnosed with coronavirus.

He announced he was entering self-quarantine about an hour after he got off the plane.

Matt Gaetz boards Air Force One for his flight with Donald Trump. Photo: AAP

Fellow representative Doug Collins also had contact with Mr Trump – shaking his hand at the Centres for Disease Control and Prevention in Atlanta on Friday.

Both men said they had no symptoms but would remain at home for 14 days.

On Sunday, senator Ted Cruz and representative Paul Gosar placed themselves in quarantine after coming in contact with the same person at CPAC.

It comes as US political leaders grapple with a public health and economic maelstrom as fears about the coronavirus outbreak escalate.

The White House said it was “conducting business as usual”, and Mr Trump sought to project calm as the epidemic poses one of the greatest tests yet to his administration.

Trump officials said they had the matter in hand, and claimed political opponents were rooting for an economic collapse.

The President shook hands with supporters on Monday when he arrived to headline a fundraiser in Florida for his re-election campaign.

He ignored shouted questions about the plunging stock market as he boarded Air Force One for the flight back to Washington.

In Monday morning tweets, he lashed out at the steep market drop and news that large public gatherings were being called off because of the virus.

“At this moment there are 546 confirmed cases of CoronaVirus, with 22 deaths,” he tweeted, comparing it to seasonal influenza and the thousands of deaths that causes.

“Think about that!”

Tweet from @realDonaldTrump

At the Pentagon, officials have begun “social distancing” measures.

On Monday, defence secretary Mark Esper’s regular meeting with senior staff, which would normally be held face-to-face in a single room with 40 to 50 participants, was broken up into three rooms, with video-teleconferencing among the rooms.

Mr Trump is delegating much of the virus response to Mr Pence, who convened a video teleconference with US governors to give an update on the federal government’s response.

-with AAP