Mr Cuomo had faced a revolt from a string of upstate sheriffs who said they would not have officers implement the rules that bans more than 10 people at family gatherings.
"I don't believe as a law enforcement officer you get to pick and choose which laws you enforce," said Mr Cuomo said in response to the criticism.
“My advice on Thanksgiving? Don't be a turkey,” he added.
Mr Cuomo also said that it was his belief that the state would see a large virus spike after Thanksgiving and urged residents to “follow the rules.”
The politician announced last week that indoor get togethers should be limited to just ten people during the holidays.
In response at least four sheriffs in Erie, Fulton, Saratoga and Washington counties said they would not have deputies enforce the rule.
“With regard to the Thanksgiving Executive Order, the Fulton County Sheriff's Office will NOT be enforcing it against our County residents,” wrote Richard Giardino on the Fulton County Sheriff's Office Facebook page.
“Frankly, I am not sure it could sustain a constitutional challenge in court for several reasons including your house is your castle.”
Erie County Sheriff Timothy Howard also said he would not send out deputies to “break up the great tradition of Thanksgiving dinner.”
But he told people in his county to “follow your heart and act responsibly.”
Saratoga County Sheriff Michael Zurlo and Jeff Murphy of Washington County both also stated that what people did inside their own homes was beyond their jurisdiction.
An advisor for Mr Cuomo urged the state’s residents to follow guidelines with their families.
"We urge everyone to continue to be smart and act responsibly. We know this makes people unhappy, but better unhappy then sick or worse,” said Rich Azzopardi.
New York is not alone in its rules and similar ones exist in neighbouring New Jersey and Connecticut.
Michigan has banned indoor gatherings of more than two households, while Vermont and Washington state have barred indoor gatherings outside immediate households.