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".
Both the Palestinian and Israeli envoys to the UN criticised the statement, for different reasons.
Brief truces offered by both Israel and Hamas punctuated the weekend, but Israeli military operations and militant rocket fire have continued.
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 Palestinian dead down by 30 after some relatives found missing family members.
Israel's military reported a new rocket attack on Monday morning, saying it had hit an open area in southern Israel.
There was a lull in the fighting in the Gaza Strip overnight, the BBC's Martin Patience reports from Gaza City, and most Gazans would have welcomed the brief respite three weeks into the conflict.
But with so many deaths and so much destruction, there is little to celebrate at Eid in Gaza, our correspondent says.
'Durable' truce
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".
It further stressed the need for "immediate provision of humanitarian assistance to the Palestinian civilian population in the Gaza Strip".
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.
"They should have adopted a resolution a long time ago to condemn this aggression and to call for this aggression to be stopped immediately," he said.
Speaking for Israel, Ron Prosor accused the Security Council statement of bias.
"Miraculously it doesn't mention Hamas," the Israeli envoy said. "It doesn't mention the firing of rockets. Those things are lacking in this statement."
Pressure on Obama
US President Barack Obama called for an immediate, unconditional humanitarian ceasefire in a phone call to Israeli Prime Minister Benjamin Netanyahu on Sunday.
Weekend ceasefires timeline
Saturday 26 July: 12-hour humanitarian truce observed by both sides from 05:00 GMT (08:00 local time) till 17:00 GMT
Israeli cabinet agrees four-hour extension until 21:00 GMT while it considers UN request for 24-hour extension, but continues operation against "terrorist" tunnels
Hamas rejects extension to 21:00 GMT because it wants "complete" stop to fighting and end to Gaza blockade
Israel announces extension of ceasefire for 24 hours till 21:00 GMT on Sunday
Sunday 27 July: Israel resumes operation in response to "incessant rocket fire" from Gaza
Hamas declares 24-hour truce, but continues rocket fire. Israel rejects ceasefire
A long-term solution, he added, would have to allow "Palestinians in Gaza to lead normal lives" and "must ensure the disarmament of terrorist groups and the demilitarisation of Gaza".
Mr Obama may have felt compelled to make the call after some embarrassment to his Secretary of State, John Kerry, in Israel, the BBC's Aleem Maqbool reports from Washington.
Mr Kerry's ceasefire plan was rejected, and his character was attacked in sections of the Israeli media.
Mr Obama may also feel that after a weekend where brief ceasefires helped expose the full extent of the destruction in parts of Gaza, he had to be seen to be condemning it, our correspondent adds.
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 had extended operations with a ground offensive, saying it was necessary to destroy tunnels dug by militants to infiltrate Israel.
Also on Sunday, the Israeli army admitted it fired a mortar round into the courtyard of a UN shelter in Gaza on Thursday in a clash with "militants", but denied it was responsible for the deaths of at least 15 people.
Despite rising concern about military casualties, support in Israel for the offensive remains widespread, the BBC's Bethany Bell reports from Jerusalem, as people see the country as being under attack.
Credit: The BBC
