Hospitals’ “usual supplies are very quickly running out,” he said.

One doctor in New York City, who was not authorized to speak publicly, recalled anguished exchanges with other physicians last week. “You’re yelling at them. You’re telling them you don’t have a dialysis machine to give them. You hear the intensity and the desperation in the other person’s voice,” the doctor said. “My job was hell.”

As the coronavirus spread rapidly in New York and in other cities, governors and mayors clamored for thousands more ventilators. But doctors have been surprised by the scarcity of dialysis machines and supplies, especially specialized equipment for continuous dialysis. That treatment is often used to replace the work of injured kidneys in critically ill patients.

The shortages involved not only the machines, but also fluids and other supplies needed for the dialysis regimen. Having enough trained nurses to provide the treatment has also been a bottleneck. Hospitals said they have called on the federal government to help prioritize equipment, supplies and personnel for the areas of the country that most need it, adding that manufacturers had not been fully responsive to the higher demand.

The fluids needed to run the dialysis machines are not on the Food and Drug Administration’s watch list of potential drug shortages, although the agency said it was closely monitoring the supply. The Federal Emergency Management Agency described the shortage of supplies and equipment as “unprecedented,” and said it was working with manufacturers and hospitals to identify additional supplies, both in the United States and overseas.

“Everybody thought about this as a respiratory illness,” said Dr. David Charytan, the chief of nephrology at N.Y.U. Langone Medical Center. “I don’t think this has been on people’s radar screen.”

The supplies allocated by manufacturers are insufficient, Dr. Charytan said, adding that the hospital switched to another type of machine when it couldn’t get additional equipment it had wanted. “It just doesn’t come anywhere close to meeting the need,” he said.