Israeli media say the country's Security Cabinet has unanimously rejected a U.S. proposal for a temporary pause in Israel-Hamas fighting.
The proposal by Secretary of State John Kerry calls for a temporary truce during which Israel and Hamas would hold indirect talks about easing the border closure of the blockaded Gaza Strip. Hamas has demanded that Gaza's crossings be opened.
Israel TV reports that on Friday evening, Israel's Security Cabinet — which groups top ministers on security issues — rejected the proposal in its current form Friday, mainly because it would mean Israel has to cut short an ongoing effort to destroy Hamas military tunnels under the Gaza-Israel border.
The latest attempts at a truce come on the heels of Israel's 18-day military operation in the Gaza Strip, fueling unrest in the West Bank where five Palestinians were killed in protests.
Despite the truce efforts, Israeli airstrikes hit more than 80 sites in Gaza, while militants in the tiny Mediterranean strip fired 50 rockets at Israel, the army said.
Among the sites hit in Gaza were 30 homes, including that of a leader of the Islamic Jihad group who was killed along with his sons, Palestinian officials said.
Israel says it wants to diminish Hamas' ability fire rockets and to destroy tunnels Hamas has dug under Gaza's border with Israel for military purposes. Hamas, meanwhile, wants to force Israel and Egypt to end their seven-year-old blockade of Gaza's borders.
The worst round of cross-border fighting in more than five years has killed 828 Palestinians and wounded more than 5,200, according to Palestinian health officials. The U.N. has civilians make up three-fourths of the dead and a majority of the wounded.
In Israel, 38 people have been killed since July 8, including 35 soldiers, two Israeli civilians and a Thai worker.
The army announced on Friday that an Israeli soldier whom Hamas had claimed to have captured earlier this week had in fact died in battle on that day. The declaration lifts fears of soldier in Hamas custody — one of Israel's worst-case scenarios in any fight with the militants.
The army said it determined that Sgt. Oron Shaul was killed among seven soldiers killed in a vehicle that was hit by an anti-tank missile in Gaza on Sunday. The others in the vehicle were confirmed dead soon after the battle ended but Shaul's remains were not immediately identified. Shaul is among the count of 35 soldiers killed in the fighting.
Meanwhile, U.S. Secretary of State John Kerry met twice Friday in Cairo with U.N. chief Ban Ki-moon and Egyptian Foreign Minister Sameh Shukri to try to bring a week-long pause in the Israel-Hamas fighting, beginning as soon as this weekend.
Kerry delayed his anticipated departure from Cairo for several hours to talk again by phone to Qatari officials who are serving as a go-between with Hamas, which the U.S. considers terrorist organization and cannot negotiate with directly.
Over the last week, in his travels from Cairo to Ramallah to Israel, Kerry made clear that he wants to secure at least a temporary truce pause before he returns to Washington.
U.S. efforts have been frustrated by distrust between Israeli and Palestinian officials and among Mideast nations that have taken sides in the conflict even as they agreed to push for a cease-fire.
The U.S. wants at least a temporary truce before it tries to usher Israel and Hamas through negotiations that could take years to resolve. The last cease-fire brokered by Egypt and the U.S. took effect in November 2012.
Hamas demands the release of Palestinian prisoners in addition to an end to the 7-year-old border blockade imposed by Israel and Egypt after the group seized Gaza from the Western-backed government of Palestinian President Mahmoud Abbas.
As the Gaza fighting drags on, the West Bank is becoming increasingly restive.
Protests erupted Friday in the northern village of Hawara, near the city of Nablus, and the southern village of Beit Omar, near the city of Hebron. Palestinian hospital officials said three Palestinians were killed in Beit Omar and two in Hawara.
The mayor of Hawara, Mouin Idmeidi, said he and hundreds of others from the village participated in a protest after emerging from a local mosque after Friday prayers.
Hawara is located along a main north-south thoroughfare that is also used by Israeli motorists. The mayor said an Israeli motorist slowed down as he passed the march and fired at the group.
The mayor said four people were wounded and that one of them, a 19-year-old, died at Rafidiyeh Hospital in Nablus of his injuries.
After the shooting, clashes erupted between Palestinians and Israeli troops who opened fire, killing a 22-year-old from Hawara, the mayor said.
Rafidiyeh hospital confirmed the deaths.
An Israeli police spokesman, Mickey Rosenfeld, said paramilitary border police opened fire to disperse violent protestsat Hawara, and that masked Palestinians threw firebombs. He said he was unaware of a shooting involving an Israeli civilian.
In Beit Omar, clashes erupted between Israeli forces and Palestinian stone-throwers. Hebron hospital officials said three Palestinians were killed.
The Israeli military said it was looking into the reports.
On Thursday, thousands of Palestinians clashes with Israeli forces at a West Bank checkpoint and in east Jerusalem, the largest protests in those areas in several years.
Associated Press writers Lara Jakes in Cairo, Mohammed Daraghmeh in the West Bank and Yousur Alhlou in Jerusalem contributed to this report.
This story has been updated.