In a later tweet acknowledging the attention his original tweet had received, Levine said he was only referring to an eventuality the city is ready for. Brooklyn and Manhattan facilities run by the city's Chief Medical Examiner "will soon be full".
NY is the USA state hit hardest by the coronavirus outbreak.
"We are NOT now planning to use local parks as burial grounds".
Hart Island in the Bronx is the location of a public cemetery housing greater than 1 million our bodies, many of them unclaimed or unidentified.
As the COVID-19 pandemic continues to claim lives in the U.S's coronavirus epicenter, every aspect of city's resources for managing the dead have been overloaded. "We are exploring using Hart Island for temporary burials, if the need grows", Goldstein responded to Levine on Twitter.
Mr Levine added: "It's not just deaths in hospitals which are up". "I've heard a lot of wild rumors, but I have not heard anything about the city burying people in parks".
Governor Cuomo warned this afternoon it was no time to relax the restrictions aimed at keeping people from getting too close to one another, and he ordered bigger fines against violators.
Not only are hundreds of people dying in hospitals, straining their morgues, but the number dying at home is exploding, said Aja Worthy Davis, a spokeswoman for the medical examiner's office.
Levine added: "It will be done in a dignified, orderly-and temporary-manner".
"This is probably going to be a very bad week", Dr Anthony Fauci, the country's foremost infectious diseases expert, said.
"This likely will be done by using a NYC park for burials (yes you read that right)", Mark Levine, the chair of the NY city council health committee, tweeted. Birx called for "less socialisation between households" and urged Americans not to go out for non-essential tasks for as long as they could avoid it. "Let's do this as a mark of respect for our awesome frontline health care workers", she said. In New York, there were 72,324 confirmed cases on Tuesday and 3,202 people had died.
The average death rate in the city prior to the novel coronavirus pandemic was 20 to 25 deaths at homes, Levine said. "But it will be tough for NYers to take", Levin wrote. "We will have the capacity for temporary burials - that's all I'm going to say".
"We are pretty full on capacity at temporary morgues and storage freezers now so it could be imminent unless we have a significant drop off in the number of deaths or an increase in capacity", Levine said.
The drop off in the attack rate in a series of communities outside the New York, New Jersey and CT areas are creating "much flatter curves", according to Birx.