Health and Human Services Secretary Alex Azar also took issue Monday with Cuomo's critique of the administration, telling Fox News that he was "disturbed" by the governor's comments.

Although Azar acknowledged Cuomo "has actually been a really good partner working with" Trump officials, the secretary dismissed the governor's comments regarding the availability of testing in New York. "There is just no factual basis for what he is saying there," Azar said.

The president's post Monday comes after Cuomo declared Saturday a state of emergency in New York as the number of coronavirus cases there surged beyond six dozen — blasting the Trump administration and New York's congressional delegation for authorizing an $8.3 billion emergency funding package that left New York with only $35 million to combat the outbreak.

Later Monday morning, Cuomo announced that the executive director of The Port Authority of New York and New Jersey had tested positive for the coronavirus. A total of 142 New Yorkers have so far become infected.

Trump's online assault also follows his targeting Friday of Washington Gov. Jay Inslee, who presides over the state that has reported 19 of the 22 deaths in the U.S. attributed to the coronavirus. Inslee declared a state of emergency last weekend, and Vice President Mike Pence hailed the governor's handling of the threat during a visit to Washington state Thursday.

But speaking Friday at the Centers for Disease Control and Prevention headquarters in Atlanta, Trump told reporters that he had urged Pence to refrain from praising Inslee, who has admonished the administration's coronavirus response.

"I told Mike not to be complimentary of that governor because that governor is a snake. So Mike may be happy with him but I'm not, OK?" Trump said.

"If we came up with a cure today, and tomorrow everything is gone, and you went up to this governor — who is, you know, not a good governor, by the way — if you went up to this governor, and you said to him, 'How did Trump do?' He would say, 'He did a terrible job,'" the president continued. "It makes no difference."

Myah Ward contributed to this report.