Mourners attend a funeral in Brooklyn, New York. AFP/VNA Photo

NEW YORK - The number of coronavirus-linked deaths in New York City soared past 10,000 on Tuesday after officials said almost 4,000 people who never tested positive were presumed to have died from COVID-19.

The city's health department announced that 3,778 people had probably succumbed to the illness -- on top of the 6,589 confirmed fatalities.

The new figures, released at 4:00pm (2000 GMT), saw the total number of deaths in the Big Apple, which quickly became America's coronavirus epicenter, soar to 10,367.

"While these data reflect the tragic impact that the virus has had on our city, they will also help us to determine the scale and scope of the epidemic and guide us in our decisions," the city's health commissioner, Oxiris Barbot, said.

The probable deaths define someone "who had no known positive lab test but with a death certificate that lists as a cause of death 'COVID-19 or an equivalent,'" according to the department guidelines.

New York state has borne the brunt of America's fast-spreading pandemic, accounting for almost half of fatalities from the crisis in the United States.

Last week, Mayor Bill de Blasio admitted that the city's official death toll probably underestimated the true extent of the deadly outbreak.

He explained that many people who had passed away at home had not been counted as having died from COVID-19 even though it had likely been the cause.

The extra deaths are also suspected to have occurred in nursing homes and other long-term care facilities.

The "probable" numbers highlight a lack of widespread of testing for the virus.

Before the city updated its toll with the likely COVID-19 deaths, New York state had reported almost 11,000 fatalities.

Hospitalisations and infections are falling, however, and Governor Andrew Cuomo has declared the "worst is over."

More than 25,400 people have died in the US, according to a running tally by Johns Hopkins University. AFP