The Israeli military and the militant Palestinian Hamas were set on Saturday to start a 12-hour ceasefire at 8:00 am (0500 GMT), but a longer-term truce remained elusive.
Hamas said that it and other militant groups in Gaza had reached "national consensus on a humanitarian truce" and Israel later confirmed that it would observe what it called "a humanitarian window in the Gaza Strip".
A statement from the Hamas-run interior ministry in Gaza warned people not to approach bombed-out buildings and militant bases for fear of "explosive objects".
Earlier, US Secretary of State John Kerry, speaking from Cairo, said that efforts to broker a longer halt to the fighting had so far yet to bear fruit.
He arrived in Paris on Saturday where France's Foreign Minister Laurent Fabius was to host a meeting later in the day of counterparts from the United States, Britain, Germany, Italy, Qatar, Turkey and the EU.
Violence, however, continued in the early hours of Saturday, the conflict's 19th day, with Israeli air strikes and shelling killing 23 people, among them four children and a paramedic, Gaza medical services said.
Kerry, who has been leading international efforts to reach a truce, said at a press conference in Cairo with UN chief Ban Ki-moon that both Israel and Hamas "still have some terminology" to agree to on a ceasefire, but added they had "fundamental framework" on a truce.
But Israel's Channel 1 TV reported late Friday that Prime Minister Benjamin Netanyahu's security cabinet had "unanimously rejected" the Kerry proposal.
The United States has worked with Egypt on a plan that, diplomats say, would provide a pause in the deadly Israel-Hamas conflict ahead of talks on key issues.
The conflict, which began July 8 when Israel launched an operation to stamp out rocket fire from Gaza and destroy Hamas tunnels, has claimed 888 Palestinian lives, most of them civilians, plus 37 Israeli soldiers, two Israeli civilians and a Thai migrant worker.
In a statement released by his office, Ban called for "an immediate, unconditional humanitarian pause in the fighting in Gaza and Israel".
"This pause would last through the Eid al-Fitr holiday period," Ban said, referring to the forthcoming Muslim festival, adding that a halt in the fighting could lead to a "longer-term ceasefire plan".
His comments tracked reports from Western and Palestinian officials of efforts to secure an initial week-long humanitarian ceasefire to be followed by negotiations on a longer-term cessation of hostilities.
- Hamas seeks end of Gaza blockade -
Signup to our newsletter and follow us on Facebook and Twitter!
Turkish Foreign Minister Ahmet Davutoglu flew to Qatar on Friday to help efforts after Kerry reached out to Hamas allies Ankara and Doha to push for a ceasefire.
Under the proposal, once a humanitarian lull takes hold, delegations from Israel and Hamas would arrive in Cairo -- which has mediated past conflicts between the two -- for indirect talks that could lead to a lasting deal.
Senior Hamas official Izzat al-Rishq said late Friday on his Facebook page the group was "studying" the idea.
Hamas's Doha-based leader Khaled Meshaal insisted in a Thursday interview with the BBC that any truce must include a guaranteed end to Israel's eight-year blockade of Gaza.
Meanwhile, in the West Bank, tensions over the situation in Gaza erupted into protests in several cities.
Israeli troops shot dead two Palestinian teenagers Saturday in separate clashes in the north and south of the West Bank.
That followed the deaths of six Palestinians and 150 injured in clashes in the West Bank Friday with Israeli troops and settlers.
- Death toll rises in Gaza -
On Thursday, at least 15 people were killed in the alleged Israeli shelling of a UN school sheltering some of the 100,000 Palestinians who have fled their homes during fighting.
The UN said it had been trying to coordinate with the army to evacuate civilians before the strike, without success, but the army said it had offered a humanitarian window, and that militants firing rockets in the area were responsible for the deaths.
Rights groups say around 80 percent of the casualties so far have been civilians, and the UN agency for children UNICEF said Friday that 192 children had been killed during the conflict.
In Lebanon, another Israeli foe, Hezbollah chief Hassan Nasrallah, made a rare public appearance in Beirut, preaching "solidarity with the people and the resistance in Gaza".
The Israeli army on Saturday announced the death of two soldiers in Gaza fighting on Friday evening.
It named one as Staff Sergeant Guy Boyland, 21, but did not give further details.
Three civilians have been killed inside Israel, by rocket fire from Gaza, which continued Saturday morning with three shot down by missile defences and one falling on open ground, the army said.
It said militants fired 60 rockets into southern Israel on Friday, with another 15 intercepted.