The Israeli military says three rockets have been fired from Gaza at Israel despite a proposed extension of a humanitarian truce in the Gaza war.
Hamas spokesman Sami Abu Zuhri said the group rejected Israel's proposal to extend an original 12-hour lull by four hours, until midnight (2100 GMT) Saturday.
The military says the three rockets were fired more than an hour after the period for the initial lull had ended.
Meanwhile, the military warned residents of areas where there had been heavy fighting against returning there.
A Hamas official says the group has rejected a four-hour extension of a humanitarian truce proposed by Israel.
Sami Abu Zuhri sent a text message to reporters Saturday, saying: "No agreement to extending the calm for an additional four hours."
Israel has set its own terms for the lull, saying it would continue demolishing Hamas military tunnels under the Gaza-Israel border.
In Paris, U.S. Secretary of State John Kerry and European foreign minister were discussing how to build on the initial 12-hour lull Saturday and transform it into a sustainable truce.
Israel's military said it would hold fire for 12 hours, but would press on with its search for tunnels used by militants. A spokesman for the Islamist group Hamas, which dominates Gaza, said all Palestinian factions would abide by the brief truce.
Hundreds of Palestinians poured into the streets in the minutes after the truce took force, some headed on foot to their homes to inspect damage from the Israeli assaults and many lined up outside banks to withdraw cash and stock up on supplies.
Fighting had continued overnight as U.S. Secretary of State John Kerry, on a visit to the region, spearheaded international efforts to end 19 days of conflict in which 883 Palestinians, many of them civilians, have been killed.
Gaza officials said five people were killed in Israeli air strikes in the night and militants fired a barrage of rockets out of Gaza, triggering sirens across much of southern and central Israel. No injuries were reported, with the Iron Dome interceptor system shooting down some of the projectiles.
Gaza Health Ministry spokesman Ashraf Al-Qidra said that 18 members of the Al-Najar family killed had been trapped inside their house in Khuzaa village east of Khan Younis since Thursday and that many others were wounded in Israeli tank shelling.
Israel said that two more of its soldiers were killed in Gaza, bringing the army death toll to 37, as troops battled militants in the north, east and south of Gaza - a tiny Mediterranean enclave that is home to 1.8 million Palestinians.
It also announced that a soldier unaccounted for after an ambush in Gaza six days ago was definitely dead, although his body had not been recovered. Hamas said on Sunday it had captured the man but did not release a photograph of him.
Three civilians have also been killed in Israel by rockets from Gaza - the kind of attack that surged last month amid Hamas's anger at a crackdown on its activists in the West Bank, prompting the July 8 launch of the Israeli offensive.
Diplomats will pursue efforts to secure a ceasefire in Paris on Saturday, with France hosting officials from the United States, Britain, Germany, Italy, the European Union, Turkey and Qatar, a French diplomatic source said.
Israel on Friday rejected international proposals for an extended ceasefire, a government source said, but Kerry, speaking in Cairo, said no formal proposals had yet been put forward.
The top U.S. diplomat said there were still disagreements on the terminology, but he was confident there was a framework that would ultimately succeed and that "serious progress" had been made, although there was more work to do.
Hamas wants an end to an Israeli-Egyptian blockade of Gaza before agreeing to halt hostilities. Israeli officials said any ceasefire must allow the military to carry on hunting down Hamas's tunnel network that criss-crosses the Gaza border.
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