Concern that President Donald Trump himself could be exposed to the coronavirus through contact with two Republican lawmakers loomed Monday as US stocks plummeted, feeding growing national anxiety.

US Vice President Mike Pence said he was unaware if Donald Trump had been tested for the novel coronavirus after it emerged that several lawmakers were exposed to the virus before meeting the president.

"I honestly don't know the answer to the question, but we'll refer that question and we will get you an answer from the White House physician very quickly," Pence told reporters. "I have not been tested for the coronavirus," Pence said in response to an earlier question.

Trump, who flew back to Washington after a weekend golfing at his Florida resort and having dinner with Brazil's right-wing president, has spent weeks dismissing the seriousness of the threat.

But after an emergency meeting with administration staff, he told journalists that he would propose "very substantial" economic measures to Congress on Tuesday. These will include tax relief and aid for workers in the gig economy who worry about calling in sick.

Trump said he would hold a press conference to discuss the measures on Tuesday, adding the coronavirus -- which has killed 26 people in the US -- has "blindsided the world."

The run on stock market prices robbed Trump of one of his main talking points ahead of the November presidential election. The Dow Jones closed 7.8 percent lower in the worst session since 2008.

And with pictures of a virus-hit cruise ship constantly on live television, Trump's tweet Monday that "life & the economy go on" seemed increasingly out of touch.

Alarm mounted further after at least two Republican lawmakers who recently met with the president announced they were going into self-quarantine, fearing that they were exposed to the virus at a conservative conference just outside Washington.

One of them, Representative Matt Gaetz, had traveled with Trump on Air Force One on Monday.

Another, Representative Doug Collins, was with Trump Friday during a coronavirus briefing at the Centers for Disease Control and Prevention headquarters.

Trump's incoming chief of staff, Mark Meadows, also went into self-quarantine Monday after learning he may also have been exposed at the same conference.

Although he is not exhibiting symptoms, and a precautionary test came back negative, "he'll be self-quarantined till the 14 day period passes Wednesday," his spokesman said on Twitter.

The spreading virus also raises questions over whether Trump will be able to continue holding the large rallies at the heart of his reelection campaign.

Trump has not been tested for the virus, White House press secretary Stephanie Grisham said Monday evening.

"He has neither had prolonged close contact with any known confirmed COVID-19 patients, nor does he have any symptoms," she said in a statement.

Stories of new cases flooded in across the country -- from a Washington DC church rector to the head of New York's ports authority, while some stores ran out of hand sanitizer and masks.

On the West Coast -- where most of the US deaths have occurred -- the Grand Princess cruise ship docked at California's port of Oakland, for more than 2,400 passengers to be taken into treatment or placed in quarantine, in a delicate, days-long operation.

- 'Business as usual' -

Grisham said there was no need for worry, denying reports that staff had been instructed to limit face-to-face meetings. "While we have asked all Americans to exercise common-sense hygiene measures, we are conducting business as usual. I want to remind the media once again to be responsible with all reporting," Grisham said.

Trump himself appeared to be less than strict about sanitary guidelines, shaking hands with well-wishers while in Florida on Monday.

Since the epidemic began, Trump has veered between defending his government from accusations of incompetence to accusing Democrats and the media of exaggerating the outbreak in an attempt to hurt his standing.

The crisis has seen him struggle to retain control over his messaging that he will ride the booming economy to certain victory in November.

On Sunday, he retweeted a meme showing himself playing the violin and the caption: "My next piece is called nothing can stop what's coming."

Trump apparently meant the meme in jest and said himself he didn't know "what this means."

Critics quickly branded it the portrait of a modern Nero -- the mad emperor famous for fiddling while Rome burned.

Trump's "reckless statements are confusing people in this country and all over the world," Democratic presidential hopeful Bernie Sanders said on the campaign trail in Michigan.

Treasury Secretary Steven Mnuchin told reporters at the White House press conference that there was no need for broader alarm, insisting that "the US has the most resilient economy in the world."

"We couldn't be more pleased that the president's economic programs of tax cuts, regulatory relief and trade have put the economy in a very good position," he said.

Trump has invited heads of major US financial institutions to a meeting on Wednesday to discuss the virus response, banking sources told AFP.