Health authorities in Gaza say 12 patients have died at the strip's largest hospital because of a lack of electricity and medical supplies.
The authorities in Gaza also noted on Sunday that many injured are losing their lives before they reach Al-Shifa hospital as fighting blocks their way. A hundred bodies reportedly remain unburied.
Another Gaza official said about 1,500 residents, who are taking shelter at the hospital, are at risk of being caught up in the fighting.
Israeli forces claim that a key command center of the Islamic group Hamas is located under the hospital.
The military says it placed 300 liters of fuel for emergency medical care at the hospital's entrance on Saturday, but that Hamas blocked the fuel from reaching hospital staff.
The Israeli military says that it urged medical staff and patients remaining at the hospital, as well as those taking shelter there, to evacuate.
In a released audio of a telephone conversation on Saturday with an official at Al-Shifa, a coordinator of the Israeli military said they are allowing for a safe exit on the hospital's eastern side, and that there are no Israeli troops in the area east of the hospital.
The Israeli military stressed that since Wednesday, it had paused the fighting for four hours at eight locations, including the Jabalia refugee camp, to allow civilians to evacuate.
It is seen as an attempt to show Israel's efforts to reduce civilian casualties amid intensifying international criticism.
Gaza authorities say 11,180 people have died in the conflict, and at least 3,250 others remain unaccounted for with some of them being trapped under rubble.
Israel says at least 1,200 people, including 361 soldiers, have been killed and about 240 are being held hostage in Gaza.