The Israeli military had told people the day before to "evacuate immediately" a part of Deir el-Balah city because it planned to "act with force against Hamas and terrorist groups" there.
Al-Aqsa Martyrs hospital sits in the middle of the area described in the warning, setting in motion a rapid exodus even though the Israeli military said medical facilities would not be affected by its operations.
Speaking to AFP on Sunday from her hospital bed outside the facility, Tamam al-Raei said she did not know where to seek safety.
"I have a war injury. I have broken bones and have had an amputation, and I have been receiving treatment for that," she said.
"But now they're telling us to evacuate Al-Aqsa. Where do we go? Where do I get treatment?"
All around her, families tried to flee, the wealthiest among them hiring donkey-drawn carts to transport their belongings.
Others carried patients in their arms, including one teenager who had lost the use of his legs and was clutching a bag of intravenous fluid.
The Israeli military said on Monday it was targeting "terror operatives" in Deir el-Balah and working to dismantle the "remaining terrorist infrastructure" of Hamas, whose October 7 attack on southern Israel triggered the ongoing war in the Gaza Strip.
'Panic and fear'
"As part of these efforts, a temporary local evacuation of the population in eastern Deir el-Balah... was carried out, for their protection," the military said in a statement.
"It should be emphasised that the evacuation efforts did not include the evacuation of hospitals and medical facilities in the area."
Gaza's hospitals have been raided by Israeli forces numerous times during their campaign to destroy Hamas.
Israel has accused Hamas of using hospitals in Gaza as a cover for military operations, claims the militants have rejected.
Memories of past violence in and around hospitals made it difficult to reassure patients and medical workers that Al-Aqsa Martyrs hospital would be safe, said Gaza health ministry spokesman Khalil al-Daqran.
"The citizens, patients and some of the medical crews were struck with panic and fear as a result of the announcement that the areas surrounding the hospital are operational areas," Daqran said.
"Therefore, a large number of patients left the hospital."
Hamas's October 7 attack on Israel resulted in the deaths of 1,199 people, most of them civilians, according to an AFP tally based on Israeli official figures.
'Nowhere to go'
Israel's retaliatory military campaign has killed at least 40,435 people in Gaza, according to the Hamas-run territory's health ministry, which does not break down civilian and militant deaths.
The UN rights office says most of the dead are women and children.
Throughout Gaza, hospitals including Al-Aqsa Martyrs have faced crippling shortages of the fuel they need to function after the territory's only power plant went out of service and Israel cut the electricity supply in the early days of the war.
Gaza's 2.4 million people, nearly all of whom have been displaced at least once, have only 16 hospitals still functioning, all of them partially.
The health situation became even more dire after authorities this month announced Gaza's first polio case in 25 years.
Families fleeing Al-Aqsa Martyrs hospital on Sunday were concerned primarily for their physical safety as they tried to adhere to repeated evacuation orders.
"We have nowhere to go, we have no refuge," Maha al-Sarsak told AFP, describing how her family had already fled multiple cities before reaching the hospital, only to leave yet again.
Iyad al-Jabri, medical director of the hospital, said his teams were not going anywhere.
"We are staying," he said.
"We will continue to treat patients and the wounded."
