Five senior US Republicans have quarantined themselves after coming into contact with a person who tested positive for coronavirus.
The members of Congress, who include Texas Senator Ted Cruz, self-isolated after they shook hands with an infected individual at a conference.
President Donald Trump, who was also at the event last month, insists he is in good health and has not taken a test.
One Democrat has also self-isolated after she met someone with the virus.
There are more than 700 confirmed cases in the US and 26 people have died so far.
Mr Cruz, Arizona Congressman Paul Gosar, Georgia Congressman Doug Collins and Florida Congressman Matt Gaetz are all self-quarantining for the recommended 14-days after they met the same infected person at CPAC, a conservative political conference, at the end of February.
Republican Representative Mark Meadows, President Donald Trump's newly appointed chief of staff, also met the person and is in self-quarantine. He is not exhibiting any symptoms and a precautionary test came back negative, a spokesman said.
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Mr Trump and Vice-President Mike Pence attended the same event in Maryland but neither of them interacted with the individual. Mr Trump did shake hands with the conference chairman who had had contact with the patient.
But, on Monday, the White House announced that Mr Trump had not been tested for the virus. "He has neither had prolonged close contact with any known confirmed Covid-19 patients, nor does he have any symptoms," a spokeswoman said.
"President Trump remains in excellent health, and his physician will continue to closely monitor him," she added.
What else did the White House say?
The White House announcement came as it warned the number of cases in the US was likely to rise. "There will be more cases," Mr Pence told reporters. "But we simply ask today for the American people to engage in the common sense practices."
The vice-president, who also confirmed he had not been tested for the virus, said the administration was consulting Congress on providing paid sick leave to workers.
Separately, in brief remarks, Mr Trump said he would take "major" steps to protect the economy against the impact of the outbreak. "We'll be discussing a possible payroll tax cut or relief, substantial relief," he told reporters.
He did not provide further details on his plans, but said there would be a news conference on Tuesday.
"This blindsided the world, and I think we've handled it very, very well," he said of the virus.
The president's comments came as stock markets plunged. Shares around the world had their worst day since the financial crisis on Monday, and analysts described the market reaction to the coronavirus as "utter carnage".
What's the latest in the US?
Cases of the virus have been recorded in 34 states plus Washington DC.
There have been 738 confirmed cases and 26 deaths, according to Johns Hopkins University.
Meanwhile, passengers aboard a virus-hit cruise liner in California have begun disembarking after being kept off the coast of San Francisco for five days.
Nineteen crew members and two passengers on the Grand Princess have tested positive for Covid-19. Most of the passengers will go into quarantine at military bases or, if they require more immediate medical attention, nearby hospitals.
Several hundred foreign passengers, including 140 Britons, will be repatriated to their home countries.
The ship's crew members will remain quarantined on board, which will depart from Oakland as soon as the passengers have disembarked, officials said.
The cruise ship came to the attention of the authorities when a previous voyager on the vessel died last week after being stricken by the coronavirus.
The 71-year-old, who had an underlying health condition, had been on a round trip from San Francisco to Mexico.
What about elsewhere?
In neighbouring Canada, as of Monday morning, there were 76 confirmed or presumptive cases of people carrying the coronavirus disease. There was one confirmed death in North Vancouver, British Columbia.
Most of the cases are in the provinces of Ontario and British Columbia, though some have also been discovered in Quebec and Alberta.
Canadian public health officials are advising against all cruise ship travel. Just last week, Canadian passengers of the Diamond Princess cruise ship were released from quarantine.
Italy now has the highest number of confirmed infections outside China, where the outbreak originated in December. It has confirmed 7,375 cases and overtaken South Korea, where the total number is 7,313.