BEIRUT — The two largest hospitals in the Syrian city of Aleppo were bombed Wednesday, knocking them out of service and worsening an already dire medical crisis in the besieged city, medical workers said.

Two patients were killed and three hospital staffers injured in the predawn attacks, including a nurse and an ambulance driver, according to the Syrian American Medical Society, which runs hospitals in opposition-controlled areas of Syria.

Since a cease-fire collapsed last week, the rebel-held eastern portion of Aleppo has been subjected to what residents describe as the most intense bombardments yet of the five-year-old war, with waves of Syrian and Russian airstrikes sending sometimes hundreds of injured people streaming to the city’s few remaining hospitals in a day.

Both of the damaged hospitals were hit by airstrikes between 3:30 and 5 a.m., according to reports from medical workers. One of the hospitals held eastern Aleppo’s only trauma center, they said.

Fewer than eight hospitals are functioning for what the U.N. estimates are 275,000 people living in the rebel-held part of the city, and there are just 29 doctors to treat the floods of injured people, said Adham Sahloul of the SAMS medical organization, who is in Gaziantep, Turkey, near the Syrian border.

Both hospitals are expected to be repaired, but they are badly damaged. It could take a while before they are functioning again. In one of them, there was extensive damage to the intensive-care unit, and a generator and ventilator were destroyed, equipment that can’t be replaced because of the siege.

Their closure, even if temporary, will deepen the already profound misery of those being injured in the bombardments, Sahloul said.

“This is going to reduce capacity. They are in areas that are hit quite often and are densely populated, so this is going to be a problem,” he said. “It is very dire.”

The pace of the bombardments has slowed somewhat in recent days after a weekend blitz that killed some 300 people and injured nearly 700. Patients piled up on the floors of the hospitals and spilled onto the sidewalks outside because there were not enough beds for such a huge influx, according to witnesses and videos and photographs posted on social media.

“We had to take the difficult decision to let the difficult cases die and attend to those who had better chances of surviving,” said Mohammed Tareq, a nurse at one of the hospitals. “Everything was topsy-turvy.”

On Tuesday, at least 26 people died in the bombardments, including 23 who were buried under the rubble of an apartment building when it was demolished by an airstrike, according to the White Helmets civil-defense group.

Aleppo has been completely encircled by government troops for the past three and a half weeks, and there are fears that medical supplies soon will run out. One hospital has already run out of anesthetics, and the surge of casualties over the past week has dangerously depleted supplies at other facilities, Sahloul said.

The bloodshed coincided with the announcement by the Syrian government that it had launched military operations to recapture eastern Aleppo from the rebels, who have controlled it since 2012, squashing any remaining hopes that the cease-fire plan could be salvaged.

The government is pressing ahead with the offensive. On Tuesday, it announced that its forces had launched a ground assault along one of the front lines near the center of the city, but no evidence showed that one had taken place.

Diplomatic efforts by the United States and Russia to solve the crisis have meanwhile lapsed since a hostile exchange Sunday at the United Nations in which the U.S. envoy Samantha Power accused Russia of “barbarism” for its support of the Aleppo assault.

Secretary of State John Kerry on Wednesday threatened to end all cooperation between the United States and Russia to stop Syria’s civil war, unless Russian and Syrian government attacks on Aleppo end. Kerry’s warning came in a telephone call Wednesday to Russian Foreign Minister Sergei Lavrov, the State Department said, describing the latest U.S. ultimatum in Syria’s 5-year conflict. Many have gone unfulfilled.

It was unclear what effect Kerry’s words would have.

“The burden remains on Russia to stop this assault and allow humanitarian access to Aleppo and other areas in need,” Kerry told Lavrov, according to State Department spokesman John Kirby.