A Palestinian doctor at a medical center in Rafah said on Tuesday that 27 bodies had been brought there since the start of Israel’s incursion, in which ground troops entered the southeast corner of Gaza and took control of the Gazan side of a border crossing with Egypt.

Dr. Suhaib Hems, the head of Kuwait Hospital in Rafah, said that his facility had also received 150 injured people, many of whom suffered from shattered bones, serious head injuries or severe burns.

“The situation is catastrophic in every sense of the word,” Dr. Hems said.

The Israeli military said it had killed about 20 people in Rafah, describing the dead as Hamas fighters. It said that “ground troops are continuing to operate against Hamas terrorist operatives and infrastructure in the area of the Rafah crossing.” Israel has called the incursion into Rafah — where more than a million people have sought refuge from the war — a limited operation.

It was not clear whether there was an overlap in the number of dead, and the two claims could not be independently confirmed.

Dr. Hem said that his hospital lacked the capacity to properly treat the wounded because of a shortage of equipment and medical staff.

“If the situation persists, we are only days away from complete service shutdown,” he said. “The health care system has completely collapsed.”

Before the war, he said, about 270 people worked at Kuwait Hospital, but that number had dwindled to just a few dozen. He said the war had left him with a feeling of “helplessness and betrayal and a sense of despair.”

According to a statement from the Gazan health ministry on Tuesday, at least 54 people had been killed across the Gaza Strip in the previous 24 hours. It said dozens more were treated for injuries at medical facilities in the territory.

“A number of victims are still under rubble and on the streets and ambulance and civil defense crews cannot reach them,” the ministry said. The circumstances of the deaths could not be confirmed independently.

Israeli forces seized control of the Rafah border crossing during the incursion and shut it down. Wael Abu Omar, a spokesman for the Palestinian side of the crossing, said the closure had prevented 46 injured and sick people from leaving Gaza for treatment in Egypt.

The patients included people with breast cancer, lymphoma and other ailments, the health ministry said.