UN Secretary General Ban Ki-moon has urged an immediate halt to violence in Gaza, saying the Palestinian territory is in a "critical condition".
"In the name of humanity, the violence must stop," he told reporters.
Shortly after he spoke, there were reports of two explosions in Gaza City - one in a children's playground and one near Gaza's main hospital.
Israel launched an offensive against Hamas militants in the territory three weeks ago after a surge in rocket fire.
More than 1,030 Palestinians, mostly civilians, and 43 Israeli soldiers and two Israeli civilians have been killed. A Thai national in Israel has also died.
Police and health officials said separate Israeli airstrikes had hit the compound of Gaza City's main hospital and a nearby playground on Monday afternoon, causing casualties.
But a spokesman for the Israel Defense Forces said both explosions were caused by misfired rockets that were launched from Gaza by "terrorists".
Mr Ban, who spoke at UN HQ in New York after returning from a visit to the region, was critical of both sides for firing into civilian areas of the small coastal strip.
He said Hamas had fired missiles into civilian areas of Israel, while Israeli forces had used high-explosive weapons in the crowded Gaza Strip.
Mr Ban said the people of Gaza had nowhere to run to, and he emphasised that participants in conflicts had a responsibility to protect civilians.
He reiterated the UN's call for an immediate, unconditional humanitarian ceasefire in Gaza during the Muslim Eid al-Fitr holiday, which marks the end of Ramadan.
Both sides had behaved in an irresponsible, "morally wrong" fashion, Mr Ban said, in allowing the violence to continue despite the efforts of the UN and US Secretary of State John Kerry.
"It's a matter of their political will. They have to show their humanity as leaders, both Israeli and Palestinian," he told reporters at UN HQ.
There were no Israeli air strikes overnight though they resumed on Monday morning after a rocket hit the southern Israeli city of Ashkelon.
Israel's military launched three air strikes on rocket sites after the rocket attack on Ashkelon. A boy aged four was killed in one of the strikes, Gaza's health ministry said.
Rockets were also fired at the Sdot Negev and Eshkol districts of Israel, Israel's Haaretz newspaper reports.
An Israeli soldier was wounded in northern Gaza where the military wing of Hamas, the Izzedine al-Qassam Brigades, said it had "clashed" with Israeli infantry.
On Sunday night, the UN Security Council called for a "durable" truce based on an Egyptian initiative, under which a pause in hostilities would lead to substantive talks on the future of Gaza, including the opening of Gaza's border crossings.
The Palestinian representative at the UN, Riyad Mansour, said the statement did not go far enough and that a formal resolution was needed demanding that Israel withdraw its forces from Gaza.
Israel's ambassador Ron Prosor accused the Security Council statement of bias for not mentioning Hamas and the firing of rockets at Israel.
Opinion polls published at the weekend suggest there is still widespread support among Israelis for the military operation.
Israel launched its military offensive on 8 July with the declared objective of stopping Hamas, the Islamist group which controls Gaza, firing rockets from Gaza into Israel.
On 18 July, it extended operations with a ground offensive, saying it was necessary to destroy tunnels dug by militants to infiltrate Israel.
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