Fearing a raid by Israeli forces, like those that have been carried out at hospitals across Gaza, the medical staff at al-Najjar rushed to relocate more than 200 patients. Some patients left in cars secured by their family members, while the seriously wounded were transferred by ambulance to other hospitals in southern Gaza, including the European Hospital in Khan Younis and the International Medical Corps field hospital in Rafah.

But even during the scramble to evacuate the hospital, Israeli airstrikes on Rafah continued. The bodies of 58 people killed in Israeli strikes arrived at the hospital since Sunday, Dr. al-Hams said, adding that the hospital staff had to ask the victims’ families to bury the bodies themselves.

“The situation is not dangerous; the situation is catastrophic, catastrophic, catastrophic,” he said.

The Israeli military’s actions also immediately limited access to more basic health services across Rafah. Project HOPE, a U.S.-based aid group that operates several clinics across Gaza, was forced to shut down a mobile medical unit within the area from which Israel has told people to leave. It had been providing primary care in the eastern part of Rafah and treating upper respiratory tract infections and gastrointestinal illnesses that had been spreading among displaced Palestinians crammed into shelters with little access to clean water and sanitation facilities.

The aid group also had to close another medical clinic elsewhere in Rafah, outside of the evacuation zone, early on Monday because six of its medical workers — including a general practitioner, a gynecologist and nurses — lived inside or immediately adjacent to where the Israeli military said it would begin its operations, said Chessa Latifi, a deputy director of emergency preparedness for Project HOPE.

Many of the medical workers had already been displaced from their homes in Khan Younis and Gaza City and were forced to flee once again with their families, including dozens of children — this time, alongside the patients they had been treating in eastern Rafah.

At least two delegations of doctors who were trying to enter Gaza on Monday to support struggling hospitals in the northern part of the enclave were forced to turn back as the security situation deteriorated, even before the Israeli military seized control of the Rafah crossing on Tuesday.

One delegation of Jordanian doctors, organized by Project HOPE, was aiming to reach Kamal Adwan Hospital in far northern Gaza to relieve overwhelmed medical staff and deliver badly needed supplies, including anesthetics, surgical sutures and gauze. That delegation was also supposed to deliver the salaries of the aid group’s medical workers in Rafah — cash they desperately needed to secure housing and transportation during the chaotic evacuation.

“We’ve had contingency plans in place for a very long time, especially as it became more and more clear that the offensive in Rafah was going to start,” Ms. Latifi said. But “the consequences of what’s happening just keep growing,” she said.

Another delegation of medical workers, organized by the aid group MedGlobal, was about halfway to Rafah from Cairo on Monday when it began receiving alerts from the World Health Organization’s coordination team that the Rafah crossing could soon be shut down.

The doctors tried to continue on their path. But once they were told that the closing of the border crossing was imminent, “most of us realized that what was going to happen was going to be significant,” Dr. John Kahler, a co-founder of MedGlobal, said.

The delegation included an anesthesiologist and a midwife who were going to support Al-Awda Hospital, one of the few hospitals still able to provide maternal care for pregnant women. Dr. Kahler himself was intending to go to Kamal Adwan, where his organization opened a nutritional stabilization center for malnourished children over the weekend.

Speaking from Cairo on Tuesday, Dr. Kahler described the difficult decision to disband the delegation. If this was the beginning of the long-threatened ground assault, he said, moving to northern Gaza from Rafah would have been too dangerous, even if the doctors were able to get through the Rafah crossing on Monday.

The level of anxiety is “sky high” among the team members and their Palestinian partners inside Gaza as they wait to see what will happen next, Dr. Kahler said.

“Babies are going to keep being delivered; injuries are going to continue to happen; people are going to continue to die,” he added.