The deaths have occurred close to the city of Seattle and are the only Covid-19 fatalities on US soil.
Four more people have died in a coronavirus outbreak in Washington state, bringing the total fatalities there to six.
These are the first deaths due to Covid-19 on US soil. Washington declared a state of emergency over the weekend.
Five of the deaths occurred in King County, whose main city is Seattle.
There are now 18 confirmed cases in the region, and there are growing fears it may spread further.
Researchers who studied the first two Washington deaths had said the virus may have been spreading there for weeks, and suggested that up to 1,500 people may have been infected.
What's the latest from Washington state?
Kathy Lofy, Washington state's health officer, said cases were confined to two counties - King and Snohomish - and the virus was "actively" spreading there. She added it was possible the virus was spreading elsewhere.
Eight of the 14 cases in King County, and four of the deaths, are linked to one care facility. Most of those who died were elderly or had underlying health conditions.
King County is to buy a hotel so it can isolate the growing number of patients in the region. More schools in the Seattle area closed on Monday.
Dr Jeff Duchin, the chief health officer for the Seattle and King County Public Health agency, said there would be no wider school closures at this stage, nor would major events be cancelled. But, he said, the number of cases is expected to increase.
"We are taking this situation extremely seriously," he said.
What's happening elsewhere in the US?
The weekend brought a sharp rise in the number of cases, raising concerns. There are now 91 confirmed cases across the country and while some patients are believed to have travelled to high-risk countries, others are thought to have contracted the virus within the US.
Late on Monday, officials said two cases of coronavirus had been confirmed in Georgia. One of the two people infected - who both live in the same household - had recently returned from Italy.
Officials on the US West Coast - in Washington, California and Oregon - have expressed concerns about infections appearing in patients who had not visited an area where there was an outbreak or been in contact with anyone who had.
The federal government has admitted to problems with its diagnostic testing amid the rise in cases. A top federal scientist has raised concerns about a possible contamination in an Atlanta, Georgia, lab where the government had made test kits for the virus, Axios reports.
Elsewhere in the US on Monday:
- New York Governor Andrew Cuomo said the state's first case was a 39-year-old female healthcare worker who had been in Iran before returning to the US last week
- The woman did not take public transportation and is not believed to have been contagious either on the plane or in the car returning home. Her spouse, also a healthcare worker, is being tested
- Officials in Florida said a man in his 60s and a woman in her 20s who had returned from northern Italy had tested positive
- President Trump met pharmaceutical companies in the White House to discuss possible vaccines
- Vide-President Mike Pence said federal officials plan to meet executives from the airline and cruise industries to discuss safeguards
What's happening around the world?
The world is in "uncharted territory" on the coronavirus outbreak, the World Health Organization (WHO) has said.
Deaths globally have passed 3,000. Most are in China but there are now far more new infections outside China than inside.
One of the countries worst affected outside China - Italy - saw a big jump in its death toll from 34 to 52 on Monday. BBC