Last week, the Trump administration announced that it was distributing an initial $30 billion in payments to hospitals and other health care providers, which is part of $100 billion set aside in the bill for them.

The administration is providing the initial $30 billion in payments to health care providers based on their past Medicare revenues — not based on how many coronavirus patients they have treated. As a result, New York is receiving far less money per coronavirus case than other states, a disparity that Mr. Cuomo highlighted last weekend.

At his daily briefing in Albany on Sunday, Mr. Cuomo pointed to a report last week by Kaiser Health News that examined how much of the $30 billion in payments would go to each state.

The report estimated that New York would get about $12,000 per coronavirus case and New Jersey would get about $18,000, while West Virginia would receive about $471,000 per case and Minnesota would get about $380,000.

In a memo last week, Kenneth E. Raske, the president of the Greater New York Hospital Association, wrote that the funding formula was “woefully insufficient to address the financial challenges facing hospitals at this time, especially those located in hot spot areas such as the New York City region.”

“It was as if everybody was treated the same, and of course under this crisis that we have, that is entirely not the case,” he said on Tuesday. “We’ve been making the case that Covid dollars should follow Covid patients. How simple is that?”

Mr. Raske said he spoke last week with Jared Kushner, President Trump’s son-in-law and a White House senior adviser, about hospital funding.