Luca Zaia, the president of Veneto, another northern region hit hard by the outbreak, warned that any country facing the outbreak needed to prepare, and said that Americans should “buy all the mechanical respirators possible to save the lives of these patients.”

He said the experience had taught Italy that coronavirus patients “are enormous consumers of oxygen” and that all of that compressed oxygen gas had led to the tubes freezing. “You can have a hospital full of reanimation beds, but if the tubes aren’t adapted, everything freezes,” he said.

At the Papa Giovani XXIII hospital in Bergamo, Dr. Ivano Riva said that for now he and his colleagues had not deprived care to anyone who could have benefited from it.

“The important thing is not to arrive at that point,” he said, adding, “No one wants to decide who lives or dies like God.”

He said 26 people on his hospital’s medical staff of 101 were out of work with the virus.

In Brescia, the hospitals have been reporting at least 350 new cases a day, Dr. Metra said Saturday. Between 10 and 15 percent of the doctors and nurses are now out sick with the virus, he said. And since the most serious virus patients require at least two weeks of hospitalization, practically the only patients who have left the hospital are those who have died.

At times, he said, his hospital has been forced to choose among multiple patients with a decent chance of survival in order to use its limited resources — mainly ventilators and the trained nurses to run them 24 hours a day — to save only a few of them.