Update at 5:35 p.m. ET.
Israel's Security Cabinet says it is willing to extend an earlier cease-fire in Gaza, NPR's Emily Harris has confirmed, until Sunday at midnight local time.
Work on neutralizing the tunnels, however, will continue, according to an Israeli official. The Israeli Defense Forces also said they will act against any violation of the extension.
A Hamas spokesman said any cease-fire that does not include the withdrawal of Israel troops from Gaza is unacceptable.
Fighting had resumed earlier when Hamas rejected Israel's offer of a four-hour cease-fire extension in Gaza and began lobbing rockets across the border, Israeli officials say.
Israeli Defense Forces said that three rockets were fired into Israel's Eshkol regional council within 15 minutes of the end of the original 12-hour cease-fire at 1 p.m. ET (8 p.m. Israeli time).
Israeli police said warning sirens sounded across the country as rockets were fired as far as the Tel Aviv area, according to Reuters.
The restart of hostilities followed an announcement by Israeli Cabinet minister Yuval Steinlitz, that the lull would be extended.
NPR's Soraya Sarhaddi Nelson reports from Jerusalem this morning that the 12-hour humanitarian cease-fire in Gaza that went into effect at 8 a.m. Israeli time (1 a.m. ET) was holding.
Hundreds of Gaza residents were taking advantage of relative calm to stock up on supplies. Some 18 days ago, Israel launched an offensive against Hamas militants in the Gaza Strip, hoping to wipe out sites launching rockets across the border and to destroy tunnels allegedly used to transport fighters and weapons. The IDF said that during the initial 12-hour cease-fire, it had uncovered four more tunnel shafts.
Reporters from The Los Angeles Times in Gaza City say "scores of bodies were pulled from [under] the rubble where they had lain for days."
Reporting from Gaza, NPR's Emily Harris says she witnessed several young men digging through rubble to recover bodies in the neighborhood of Shejaia, which has saw intense fighting and heavy casualties, particularly in fighting that occurred last weekend.
"We came across one house that had been crushed and underneath a slab of concrete which had landed at an angle to the ground," Emily tells Weekend Edition Saturday. "There was a knot of young men in bare feet and sandals using hand tools and their hands to try to dig out a third body, they had recovered two bodies already.
"Today, people were flooding into Shejaia. There were traffic jams for the first time since this war has been on. They were going to their homes, recovering what they could and then leaving," she said.
There is, for the moment, enough food and water, she says: "There aren't many shops open, but there hasn't been a real food crisis here. The United Nations schools, which are housing 160,000 people as of last night are facing pressure to get clean drinking water a lot of it has to be trucked in."
But, despite Saturday's cease-fire, Israeli forces in Gaza are continuing to search out and eliminate the Hamas-built tunnels. The Israeli military says it has uncovered 31 concrete-lined tunnels so far, 11 of which were destroyed, Soraya says.
The West Bank and Jerusalem are also quiet following a number of Palestinian protests against Israel Friday that led to at least five people being killed.
A Hamas spokesman says all Palestinian factions will abide by the temporary cease-fire.
Nearly 1,050 Palestinians, mostly civilians, have been killed in the fighting and almost 6,000 wounded, according to Ashraf al-Kidra, a spokesman for the health ministry in Gaza. He said 85 bodies had been recovered since the beginning of the cease-fire. Israel says 37 of its troops and three civilians have been killed.
News of the truce came on Friday after extensive and so far unsuccessful U.S. efforts to reach a broader truce. Despite reports by Israeli media that a deal being brokered by U.S. Secretary of State John Kerry for a seven-day cease-fire had collapsed, Kerry insisted on Friday that it was only a matter of working through the details.
"They may have rejected some language or suggestion, but there was no formal proposal submitted by me on which a vote was ripe," he said.
"There's always mischief from people who oppose things. So, I consider that a mischievous leak," Kerry said of the reports that Israel's Security Cabinet had rejected the truce proposal outright.
Foreign ministers from seven nations have called for an extension of the cease-fire, according to Reuters, which quotes France's Laurent Fabius as saying "All of us call on the parties to extend the military cease-fire that is currently underway."
As The Associated Press notes: "[The] temporary lull was unlikely to change the trajectory of the current hostilities amid ominous signs that the Gaza war is spilling over into the West Bank."
"In a 'Day of Rage,' Palestinians across the territory, which had been relatively calm for years, staged protests against Israel's Gaza operation and the rising casualty toll there. In the West Bank, at least six Palestinians were killed by Israeli fire, hospital officials said."