In an interview on Fox News on Thursday, Mr. Trump scoffed at New York’s claim that it needs at least 30,000 ventilators — machines that help the sickest patients keep breathing — to fight the crisis. State officials have repeatedly asked the federal government to help close a shortfall they have estimated at more than 20,000.

“You know, you go into major hospitals, sometimes they’ll have two ventilators and now, all of a sudden, they’re saying, ‘Can we order 30,000 ventilators?’” Mr. Trump said in the interview. “I don’t believe you need 40,000 or 30,000 ventilators.”

Mayor Bill de Blasio said on Friday that Mr. Trump failed to grasp the outbreak’s severity. “He’s not looking at the facts of the astronomical growth of this crisis,” the mayor said on ABC’s “Good Morning America.”

As of Friday morning, 1,583 coronavirus patients in New York State were in intensive care units, nearly all of them on ventilators — a number that has almost doubled in two days. The state has projected that the need for I.C.U. beds will grow for at least several weeks.

“The only way we can obtain these ventilators is from the federal government,” Mr. Cuomo said this week. “Period.”

In a survey released on Friday, the United States Conference of Mayors found that 85 percent of American cities did not have an adequate supply of ventilators.