Israeli forces bombarded a Gaza refugee camp on Friday after a deadly strike on a UN-run school there, as the war sparked by Hamas's unprecedented attack on Israel entered its ninth month.

The conflict has killed thousands, laid waste to much of the Gaza Strip, uprooted most of its 2.4 million people and put them at risk of starvation.

Efforts to mediate the first ceasefire since a week-long pause in November appear to have stalled, only a week after US President Joe Biden offered a new roadmap.

Hamas has yet to respond to Biden's proposal, while Israel has expressed openness to discussions but remains committed to its goal of destroying the Palestinian Islamist group.

Al-Aqsa Martyrs hospital in Deir al-Balah, central Gaza, said at least 37 people were killed in Thursday's Israeli strike on the UN-run school in Nuseirat camp.

The Israeli military said its fighter jets killed nine "terrorists" who were hiding in three classrooms.

The United Nations agency for Palestinian refugees, UNRWA, said hundreds of displaced Gazans were sheltering at the school, which was "hit without prior warning".

UN Secretary-General Antonio Guterres described the strike as "horrific", while Egypt's foreign ministry spokesman Ahmed Abu Zeid condemned what he called the "deliberate bombing of an UNRWA school".

"Israeli violations of Palestinian rights continue day after day, in full view of the civilised world," Abu Zeid said on X.

The United States, which provides Israel with $3.8 billion in annual military aid, urged its ally to be "fully" transparent about the strike.

Israel accuses Hamas and its allies in Gaza of using schools, hospitals and other civilian infrastructure, including UN-run facilities, as operational centres -- charges the militants deny.

An Israeli strike late Thursday killed Nuseirat mayor Iyad al-Mughari as he was visiting a water pumping station, a municipality spokesman said Friday.

Israel's military said it would publish a statement about the strike.

A day after the school was hit, eyewitnesses said the Nuseirat refugee camp came under attack again as Gaza faced Israeli attacks from land, sea, and air.

Witnesses also reported Israeli strikes east of Deir al-Balah and intensive fire from army vehicles near the Bureij camp, where a blaze was raging.

The Israeli military said it "eliminated dozens of terrorists" in eastern Bureij and Deir al-Balah, where a hospital source said a strike on the Wafati home in nearby Maghazi camp killed six people.

The military also released footage of soldiers conducting operations in bombed-out buildings in the southern city of Rafah.

Fighter jets targeted Al-Sultan neighbourhood, said sources in the city bordering Egypt.

Gaza also came under fire from the sea, with Israeli warships bombarding homes in the fishermen's port and other areas west of Gaza City, an AFP correspondent said.

Osama al-Kahlut of the Palestinian Red Crescent Society said "occupation forces and snipers" east of Deir al-Balah were firing on people along Gaza's main thoroughfare.

"Gunfire on Salaheddin Street has severely restricted people's movement, and several wounded people have been evacuated from the area," he told AFP.

Israel has faced growing diplomatic isolation, with international court cases accusing it of war crimes and several European countries recognising a Palestinian state.