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With thousands of coronavirus deaths in New York nursing homes, New York Gov. Andrew Cuomo is feeling the heat – even as an accounting of those fatalities remains woefully incomplete.

Cuomo, widely praised for his efforts to contain the coronavirus, has been roundly criticized more recently over a policy that critics say exacerbated the spread of the virus in New York's 613 state-regulated nursing homes.

The policy required nursing homes to accept recovered COVID-19 hospital patients. The aim was to ease the burden on hospitals treating coronavirus patients. On May 10, New York reversed the policy amid criticism and the mounting death toll.

The state has reported nearly 23,000 COVID-19 deaths. As of Sunday, New York’s nursing home COVID-19 death toll stood at 5,601, an increase of 203 in six days. The COVID-19 tally was reported as 2,955 confirmed deaths and 2,646 presumed deaths.

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New York Gov. Andrew Cuomo briefs the media at Marist College, on Friday, May 8. (AP/Office of Governor Andrew M. Cuomo)

But the figure for nursing home deaths doesn’t include nursing home residents who die in hospitals.

“I am concerned that not reporting deaths of residents who have gone to the hospital hides the extent to which COVID-19 is spreading in facilities,” Richard Mollot, of the Long Term Care Community Coalition, an advocacy group for nursing home residents, told Fox News.

“I am equally concerned about the numbers of residents who are suffering and dying due to abject neglect and deteriorating conditions resulting from facilities being understaffed, but continuing to accept or retain residents for whom they cannot provide safety and care,” he said.

Even as news outlets reported the total confirmed and presumed COVID-19 deaths in New York nursing homes, Cuomo spokesman Peter Ajemian criticized the way the number was tallied.

A NYPD officer wears a mask to protect against coronavirus, stands watch as May Day protestors gather outside the offices of New York Gov. Andrew Cuomo,  May 1, in the Manhattan borough of New York. (AP Photo/John Minchillo)

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"The death number is not right – that combines probable and confirmed – no other state reports that – please only use confirmed," he said to Fox News.

The Daily Caller reported Friday that New York had tallied deaths of nursing home residents in nursing homes and in hospitals, citing an April 28 New York Department of Health document found on a web archive.

The website reported being told by a N.Y.D.H. spokeswoman that the state was opting not to disclose out-of-facility deaths “in order to maintain consistency and reliability in the data as presented, and to avoid any potential for double-counting.”

The department did not respond to a request for comment from Fox News.

Cuomo's response to the coronavirus at the start of the pandemic also was faulted in a new report.

A train conductor wears a protective mask while riding on a subway through the Fulton Street station on May 6 in New York City. (Photo by Stephanie Keith/Getty Images) (Getty Images)

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On Saturday, ProPublica published a lengthy story that explored the strained relationship between Cuomo and New York City Mayor Bill de Blasio, and contrasting New York's response to the pandemic to California's, which has far fewer COVID-19 deaths.

As of May 15, there were nearly 350,000 COVID-19 cases in New York and more than 27,500 confirmed and presumed deaths, nearly a third of the nation’s total, ProPublica reported. California has just under 75,000 cases and slightly more than 3,000 deaths.

A Cuomo official told the news outlet in response that from the discovery of the first positive COVID-19 case in New York on March 1 to the shutdown on March 22, New York had acted faster than any other state.

“Three weeks, 20 million people,” the official said. “Insane.”

Criticism also was leveled at Cuomo after his aides inserted into New York's 2021 budget a provision giving nursing homes immunity from coronavirus lawsuits.

On Monday, New York City Assemblyman Ron Kim introduced legislation to repeal the provision. Kim represents a Queens district with a number of nursing homes.

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“Behind closed doors and in secrecy, nursing home executives managed to push Gov. Andrew Cuomo into adding a provision in this year’s budget that insulates them from criminal or civil liability during the COVID-19 pandemic,” Kim said, according to QNS.com. “The executives running the nursing homes knew back in mid-March that their facilities could not keep their residents safe; they sought to protect their businesses and themselves from their expected negligence.”

Long Island State Veterans Home in Stony Brook, L.I. (Google Maps)

On Monday at his daily coronavirus news briefing, Cuomo appeared to walk back remarks he made the previous day saying older people are going to die from the virus, "despite whatever you do," according to WRGB-TV.

That angered a lot of people, the station reported.

"Protecting our nursing homes and our seniors has been a top priority,” Cuomo said Monday. “Last week, I put a requirement in place that staff at nursing homes be tested twice a week ... all staff."

The governor added, "You will always have people who say we should do more. That always happens, and by the way, now they're complaining we're doing more and they want it both ways. You can't have it both ways."

Initially, when it came to providing an accounting of nursing home fatalities, the Cuomo administration refused, citing health privacy laws.

Then in mid-April in response to media demands for the information, the N.Y.H.D. released a list of 72 nursing homes and assisted living centers where 1,135 residents had died.

“Some homes included presumed COVID-19 deaths as well as confirmed COVID-19 deaths,” the health department said.

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But the list only identified facilities with more than five deaths and only accounted for fatalities that occurred in a facility.

Nursing homes with fewer than five deaths weren’t identified out of privacy concerns, Jim Malatras, a member of Cuomo's coronavirus task force, said at the time.

Families of nursing home residents also found inaccuracies in some of the data. Several nursing homes that self-reported more than 20 deaths weren’t on the list.

In early May, New York released a revised set of data showing 4,813 people died in state nursing homes from COVID-19, a jump of 1,700 in one day.

The new data included confirmed and presumed deaths from each nursing home. It also listed nursing homes with fewer than five deaths.

The total didn’t include nursing home residents who died in hospitals. Daily updates still don't tally those deaths.

As of May 17, Ferncliff Nursing Home in Rhinebeck has reported 13 confirmed and presumed COVID-19 deaths.

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But the count is missing Dolores McGoldrick, 89, who lived at Ferncliff and died in April at a hospital after contracting COVID-19, the Ithaca Journal reported May 2.

Her daughter Kathleen Cole, a nurse, told the paper her mother was infected shortly after a fellow nursing home resident was re-admitted to Ferncliff from a hospital in late March.

Cole said the nursing home staff told her the other resident didn't have COVID-19 when re-admitted but didn't provide many other details about the case, the paper reported.

She now blames her mother’s death on the entire nursing home system – from Ferncliff's inability to contain the virus to state officials' refusal to release many details about infections and deaths at the facility and other nursing homes, according to the paper.

"The whole thing has just been handled awfully ... by everybody in regard to nursing homes," she said. "It's like a slaughterhouse at these places."

Ferncliff spokesman Jon Goldberg declined to discuss a specific resident's case, citing health privacy laws, according to the paper.

Many New York nursing homes have refused media requests for information on coronavirus cases and deaths in their facility or declined to respond.

An exception has been the Long Island State Veterans Home in Stony Brook, which reports the information in letters addressed to LISVH family members.

On Friday, the facility posted its most recent letter saying 74 residents had died of COVID-19, one of the highest totals in the state.

But the state's latest list shows LISVH having 51 confirmed and six presumed COVID-19 deaths.

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“Our veterans are our heroes,” LISVH executive director Fred Spanga wrote in the letter. “Each of them understood the value of freedom and answered the call.”