Over 300 people were evacuated from the ship, which is docked and held in quarantine near the port of Yokohama, Japan. Charter flights carrying the evacuees landed at two air force bases in California and Texas on Sunday and Monday.
In a joint statement from the US Departments of State and Health and Human Services, officials said they were notified of the 14 positive cases during the evacuation process, after passengers disembarked the ship.
The agencies said: “After consultation with HHS officials, including experts from the HHS Office of the Assistant Secretary for Preparedness and Response, the State Department made the decision to allow the 14 individuals, who were in isolation, separated from other passengers, and continued to be asymptomatic, to remain on the aircraft to complete the evacuation process.
“Any who become symptomatic will be moved to the specialised containment area, where they will be treated.”
All passengers who have not tested positive for the virus or developed any symptoms since landing will remain under quarantine for 14 days.
The US was the first country to evacuate its passengers from the cruise ship, which was ordered to stay under quarantine off Japan on 3 Feb.
454 people have tested positive for coronavirus on the Diamond Princess cruise ship, the largest cluster of cases outside China so far.
There are more than 70 Britons on the ship at present. Downing Street confirmed on Monday they are being contacted about the possibility of a repatriation flight.
Globally, coronavirus has infected over 71,000 people and claimed the lives of 1,775 people, mostly in China where the outbreak began.