Mr Cuomo's original order was issued on 25 March. It effectively barred nursing homes from turning away individuals "solely based on a confirmed or suspected diagnosis of Covid-19."
Fox News reported that the webpage where the order was recorded was removed or moved sometime after 5 May.
Mr Cuomo has been the subject of criticism due to the high number of Covid-19 deaths in nursing homes in his state. New York accounts for 5,300 of the 26,000 nursing home deaths nationwide.
He defended his actions, claiming he was simply following the guidance put forth from the White House.
"New York followed the president's agencies' guidance," he said. "What New York did was to follow what the Republican Administration said to do. That's not my attempt to politicize it. It's my attempt to depoliticize it. So don't criticize the state for following the president's policy."
The policy Mr Cuomo is referring to is a directive issued 13 March from the Centers for Medicare & Medicaid Services - a part of President Donald Trump's presidential administration - and the US Centers for Disease Control and Prevention. The directives were issued to all states and provided guidance on how to keep infections under control in nursing homes.
Mr Cuomo's communications director defended the governor's actions, saying that Mr Cuomo wasn't trying to hide or rescind the order, but expanded the directive.
"He didn't reverse or rescind anything. The order is still in effect. He did add a directive, this one direct at hospitals, saying they must test patients and the patient must be negative before being sent back to a nursing home," Peter Ajemian, Mr Cuomo's comms director, told Fox News. "And he is requiring nursing homes to test staff twice a week."
The new directive Mr Ajemian is referencing was introduced on 10 May. He said the language from the original guidance was removed because it seemed contradictory and caused confusion.
"[The Department of Health' posted updated guidance that builds on the original 25 March guidance which barred nursing homes from discriminating against Covid patients," Mr Ajemian said. "Then and now, nursing homes cannot discriminate against COVID patients and they cannot accept patients if they aren't able to provide adequate care, including staff screenings, PPE and infection control measures like cohorting."
Mr Ajemian said the new guidance didn't supersede the 25 March directives, but "added a new requirement that says hospitals cannot discharge patients to nursing homes until they test negative."
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