Sporadic attacks by both Israel and Palestinian militants have punctuated a lull in fighting after the quietest night in the 21-day conflict.
There were no Israeli air strikes overnight though they resumed in the morning after a rocket hit the southern Israeli city of Ashkelon.
Earlier the UN Security Council urged a halt to hostilities to coincide with the Muslim holiday of Eid al-Fitr.
Israel launched its offensive 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.
The Security Council called on Sunday night for an "immediate and unconditional humanitarian ceasefire" in Gaza over and beyond the holiday period.
Both the Palestinian and Israeli envoys to the UN criticised the statement, for different reasons.
The UN Security Council has called for an "immediate and unconditional humanitarian ceasefire" in Gaza.
An emergency session backed a statement calling for a truce over the Muslim holiday of Eid al-Fitr "and beyond".
On Sunday Israel and Palestinian militants continued their offensives despite a 24-hour ceasefire announced by Hamas.
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. The Gaza health ministry on Sunday revised the number of dead down by 30 after some relatives found missing family members.
The UN Security Council endorsed a statement from Rwanda, the current president of the council, calling 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 statement also emphasised that "civilian and humanitarian facilities, including those of the UN, must be respected and protected".