As passengers disembark, President Trump proposed tax cuts to help the economy weather the crisis.
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.
The vessel carrying 3,500 people from 54 countries, has docked in Oakland.
The US has reported more than 607 coronavirus cases and 24 deaths. President Donald Trump said it had "blindsided" the world.
Cases of the virus have been recorded in 34 states plus Washington DC.
Some US politicians - including Mr Trump's newly appointed chief of staff Mark Meadows - are self-isolating after coming into contact with an individual who has tested positive.
The number of infections worldwide is more than 109,000, with about 3,800 deaths.
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.
Some 16 million people - a quarter of Italy's population - are under strict quarantine measures.
The Grand Princess cruise ship came to the attention of 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 in February.
The operation to move passengers from the Grand Princess is due to be completed on Tuesday.
Passengers requiring urgent medical care are being taken to hospital first. Then US residents not needing treatment will be moved to military bases in California, Texas and Georgia for a 14-day isolation period.
Several hundred foreign passengers, including 140 Britons, will be repatriated to their home countries.
The UK Foreign Office said it was "working intensively" with US authorities to arrange a flight for British nationals which is currently expected to leave the US on Tuesday evening and return to the UK by Wednesday afternoon.
Passenger Linda Stennett, from Shrewsbury, told BBC Radio Shropshire the Foreign Office had confirmed in an email that they would be sending a plane to repatriate Britons.
"We know when we dock, that the Americans will be getting off first and that is going to take, they reckon, two to three days, and I think we are after that, hopefully."
Ms Stennet said morale is good on board, but that passengers are "going a bit stir crazy" after being confined to their rooms for so long.
The Canadian government will be also repatriating over 200 Canadian nationals on the vessel. All asymptomatic Canadians will be flown home and placed under 14-day quarantine at a military base in Ontario.
Any symptomatic individuals will be further screened and may be treated in the US, Canadian officials said.
The ship's crew members will remain quarantined on board, which will depart from Oakland as soon as the passengers have disembarked, officials said.
"No one will be quarantined in Oakland, or released to our community," Oakland mayor Libby Schaaf told a news conference.
The ship is operated by Princess Cruises, which also owns the Diamond Princess, which was placed into quarantine in Japan last month.
Several other Princess Cruises have been blocked, with the Regal Princess held off the coast of Florida until coronavirus testing is completed.
Another cruise ship, the Costa Fortuna, with around 2,000 aboard, was turned away by Malaysia and Thailand, an official said.
Coronavirus hits US capital
The virus' spread has also reached Washington DC, affecting lawmakers and locals - and putting President Donald Trump only two degrees of separation away from the outbreak.
The first confirmed case of Covid-19 in the capital is a church rector in his 50s. DC officials on Monday urged the several hundred members of Christ Church Georgetown to voluntarily self-quarantine for 14 days.
The second DC case is a man currently in hospital in Maryland who had stayed in the capital for a night before being diagnosed.
Four Republican lawmakers - Texas Senator Ted Cruz, Arizona Congressman Paul Gosar, Georgia Congressman Doug Collins and Florida Congressman Matt Gaetz - are also self-quarantining after shaking hands with an infected individual at a conservative political conference at the end of last month.
Mr Trump and Vice-President Mike Pence also attended the event. While neither directly interacted with the individual, Mr Trump did shake hands with the conference chairman who had had contact with the patient.
And Mr Gaetz boarded the presidential plane Air Force One with Mr Trump on Monday before announcing that he had been tested for the virus.
At a news conference on Monday evening, Mr Pence was asked if President Trump had been tested, but he was unable to say.
The president has continued to urge calm in the midst of the outbreak, taking to Twitter on Monday to compare Covid-19 to the common flu.
The president told reporters that he was proposing measures to cut taxes to support the economy.
"We'll be discussing a possible payroll tax cut or relief, substantial relief, very substantial relief, that's a big number," Mr Trump told the White House briefing.
What's the situation in Canada?
As of Monday morning, there were 76 confirmed or presumptive cases of people carrying the coronavirus disease in Canada, including 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. BBC