Workers in protective gear are toiling to bury dozens of bodies in mass graves on an island in Long Island Sound, as New York City deals with a mounting coronavirus death toll and dwindling morgue space.

Key points: Coffins are being buried in trenches on Hart Island, off the Bronx

Coffins are being buried in trenches on Hart Island, off the Bronx New York state's daily death toll hit 799

New York state's daily death toll hit 799 But the rate of people being hospitalised has slowed dramatically

Aerial images showed workers putting coffins into trenches on Hart Island — a 1.5 kilometre-long island off the Bronx where more than a million mostly homeless and poor New Yorkers have been buried over the years.

Typically, about 25 bodies a week are buried on the island, mostly for people whose families can't afford a funeral, or who go unclaimed by relatives.

Burials are now happening five days a week, with around 24 burials each day, according to the Department of Correction.

About 40 coffins were lined up for burial on the island on Thursday, and two fresh trenches had been dug in recent days.

New York continues to be hit hard by the coronavirus outbreak, with the state posting a record-breaking increase in coronavirus deaths for a third consecutive day on Thursday, even as a surge of patients in overwhelmed hospitals slowed.

The number of deaths in the state of New York rose by 799 to more than 7,000, after increases of 779 the day before, and 731 the day before that.

New York City Mayor Bill de Blasio said that if the city ran out of morgue space, bodies could be temporarily individually buried on Hart Island and families would be able to reclaim them at a later date.

But the city's medical examiner's office said it did not anticipate running out of space in morgues.

New Yorkers were warned not to relax despite the daily rate of hospitalisations slowing. ( AP: John Minchillo )

'No, you can't relax,' warns NY's Governor

New York Governor Andrew Cuomo described Thursday's death count as a lagging indicator, reflecting the loss of people who became sick earlier in the outbreak.

The snapshot of hospitalisations showed a less dire picture.

A net 200-patient increase in hospitalisations was "the lowest number we've had since this nightmare started", Mr Cuomo said, compared with daily increases of more than 1,000 last week.

New York Governor Andrew Cuomo says the state is not "out of the woods yet". ( Reuters: Carlo Allegri )

More than 18,200 people were in hospital with COVID-19 symptoms on Thursday, and intensive care admissions were also down.

"Today we can say that we have lost many of our brothers and sisters, but we haven't lost anyone because they couldn't get the right and best health care that they could," Mr Cuomo said at his daily news briefing.

Mr Cuomo and Mr de Blasio used the same metaphor that New York was not "out of the woods" yet at successive briefings on Thursday.

"It is good news. 'Well, now I can relax,' No, you can't relax," Mr Cuomo cautioned.

"The flattening of the curve last night happened because of what we did yesterday and the day before and the day before that."

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Mr de Blasio said New York City needed to continue social distancing as well as adding more coronavirus testing capacity before the loosening of restrictions could be considered.

"If we really work hard we have a chance of seeing change in May or June," he said.

From Monday the city will release ongoing data on three key virus indicators: the number of people admitted to hospitals and suspected of having COVID-19; the number of intensive care unit admissions for the disease; and the percentage of coronavirus tests that come back positive, Mr de Blasio said.

All three numbers would have to go down in unison for 10 days to two weeks before the city could consider loosening social distancing restrictions.

But in order to contemplate returning to anything approaching normalcy, the city would also need to be able to test more people for the virus, he added.

"We need some greater capacity," he said.

"I think the Federal Government is still the most important part of this equation when it comes to testing."

AP/ABC