At a news conference where he announced that another 391 people in the state had died of the virus over the last day, bringing the state’s total to 1,941, and the tri-state region’s to 2,381, Mr. Cuomo said that the state was still struggling to get the ventilators and other medical supplies it needs.

“Really, the only hope for a state at this point is the federal government’s capacity to deliver,” Mr. Cuomo said, going on to discuss the powers that the Defense Production Act, a Korean War-era law, gives the president to procure vital equipment.

In recent days a chorus of governors from across the political spectrum have publicly challenged the Trump administration’s assertion that the United States is well stocked and well prepared to test people for the virus and care for the sickest patients. In many cases, the governors said, the country’s patchwork approach had left them bidding against one another for supplies.

Gov. Larry Hogan of Maryland, a Republican, said on Tuesday that his state was “flying blind” in the fight against the coronavirus because officials did not have enough tests. When asked during an NPR interview about Mr. Trump’s recent comments suggesting that a chronic lack of test kits was no longer a problem in the United States, Mr. Hogan did not mince words: “Yeah, that’s just not true.”

Gov. Ned Lamont of Connecticut, a Democrat, said on Tuesday that it was “disturbing” to learn that a national stockpile of medical supplies was running empty.

“We are on our own,” he said.

As the crisis has grown more dire across the country, Mr. Cuomo’s briefings, which have become a daily staple of the national news and raised his political profile, have taken on a broader purview.

On Wednesday, the governor again emphasized the regional coordination between his state, New Jersey and Connecticut, before noting that the virus was spreading more rapidly in other states, including California, Michigan and Florida.