Mr. Trump and other Republicans have also sought to blame the coronavirus outbreak on the W.H.O., which Mr. Cuomo singled out by name, too. The W.H.O., which first identified the virus as a pneumonia of unknown cause on Jan. 5, did not return requests for comments on the governor’s remarks.

Mr. Cuomo has largely been praised for the magnanimous tone he has usually tried to strike in his daily briefings, often saying it is not the time for recrimination or politics, a topic he mused about earlier this month while quoting the Bible and Abraham Lincoln.

“This is no time and no place for division,” Mr. Cuomo said on April 18. “We have our hands full as it is.”

Mr. Cuomo’s handling of the crisis in New York, where more than 17,500 people have died, has resulted in a spike in his popularity, but more critical evaluations of the state’s overall response have increasingly emerged with the mounting death toll, particularly in comparison with other states and cities that have had less serious outcomes thus far.

The governor has argued that the state was quick to respond to the outbreak, noting it shut down nonessential businesses and ordered residents to stay at home as of the evening of March 22. That was three days after a stay-at-home order went into effect in California, a state with more than twice the population of New York but about a tenth of the confirmed deaths, and about a sixth of the cases.

The governor had previously wondered aloud about responsibility for detecting the virus, saying in mid-March that “we knew this was happening in China back in November” and noting how air travel could spread the disease.

The state’s first guidance on the outbreak came on Jan. 17, when the state’s Health Department issued a one-page sheet for health care providers, along with information from the C.D.C.