"We have been able to control the fire in the hospital but not in the administrative building," one hospital official said.
"We hope that the flames don't spread again to the wings of the hospital."
Two hospitals east of Gaza City were also hit by Israeli shells as Gazans fled tanks advancing into the city.
It was not immediately clear if any casualties following the raids.
UN fire 'still raging'
The Israelis also bombed a UN compound in Gaza City, setting fire to warehouses of badly-needed food and medical aid and prompting international outrage.
Around 700 Palestinians were sheltering in the UN complex at the time of the strikes which left two civilians and three staff members injured.
Adnan Abu Hasna, a spokesman for the United Nations Relief and Works Agency (Unrwa), said fires were still raging hours after the attack and "tens of millions of dollars worth of aid" had been destroyed.
John Ging, the director of Unrwa operations in the Strip, also accused the Israelis of using phosphorus shells.
"They are phosphorus fires so they are extremely difficult to put out because, if you put water on, it will just generate toxic fumes and do nothing to stop the burning," he said.
Israel insists all weapons used in the conflict comply with international law.
The attacks came as the number of Palestinians killed in Israel's offensive reached 1,095 with more than 5,100 wounded.
More than 330 children are among the dead and nearly half are civilians.
Thirteen Israelis have died, three of them civilians.
Two buildings housing international journalists in Gaza have also been bombed by Israeli forces.
'Investigation needed'
Ehud Olmert, the Israeli prime minister, justified shelling the UN headquarters claiming armed Palestinians within it had fired at Israeli troops first.
"It is absolutely true that we were attacked from that place … but the consequences were very sad and I apologise for it," he said.
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"There were no militants in our compound and... [the Israelis] are changing their story saying militants were 'in the vicinity'"
Christopher Gunness, Unrwa spokesman
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However, Christopher Gunness, a spokesman for Unrwa, robustly denied that Palestinian fighters were among refugees sheltering there.
"At no stage during the fighting today did any Israeli official pick up the phone and tell us there were militants in our compound.
"We always take action against militants ... there were no militants in our compound and now they [the Israelis] are changing their story, saying militants were 'in the vicinity'," he said.
Gunness called for a "proper investigation" into the incident.
Louis Michel, the European Aid Commissioner, also condemned the bombing of the UN complex, branding it "unacceptable".
"I am deeply shocked and dismayed to learn of this incident ... I have made it very clear that all sides must respect international humanitarian law.
"It is unacceptable that the UN headquarters in Gaza has been struck by Israeli artillery fire," he said.
Ban Ki-moon, the UN secretary general, strongly condemned the incident and demanded a full explanation from Tzipi Livni, the Israeli foreign minister, during talks held on Thursday in Tel Aviv.
Ban said Ehud Barak, the Israeli defence minister, had apologised for the attack describing it as a "grave mistake".
A Red Crescent office near Gaza City and the main mosque in the southern city of Rafah were also shelled as the Israelis pushed deeper into the Strip.