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The Israeli military estimated on Wednesday (local time) that accomplishing that task would take several more days, extending a four-week-old aerial and ground offensive in the small, densely populated coastal territory.
"We are determined to complete this mission, with or without a ceasefire," Netanyahu said in public remarks at a meeting of his full cabinet in Tel Aviv. "I wont agree to any proposal that will not enable the Israeli military to finish this important task, for the sake of Israel's security."
Leaving open the option of widening its ground campaign in the Islamist Hamas-dominated Gaza Strip, the Israeli military said it had called up an additional 16,000 reservists. They will relieve a similar number of reserve soldiers being stood down, a military source said.
Fighting, however, appeared less ferocious than on previous days this week - more than 100 were killed on Wednesday alone.
Gaza health officials said 34 Palestinians were killed in Israeli assaults on Thursday that included an air strike on a home in the Nuseirat refugee camp in the central Gaza Strip, killing 11 members of the same family.
The Israeli military said more than 90 rockets were fired from the Palestinian enclave, some deep into Israel. One person was moderately wounded by a Gaza projectile that struck in the southern town of Kiryat Gat.
Three Israeli soldiers were wounded, one critically, by a cross-border mortar, Barzilai hospital director Hezi Levi told Channel Ten television. Israeli media said at least three more people hurt in the attack but the military gave no details.
Hamas said it had fired one rocket at Israel's commercial hub Tel Aviv, which the military said was intercepted.
Israel launched its offensive in Gaza on July 8 in response to a surge of cross-border rocket attacks.
Gaza officials say at least 1,427 Palestinians, most of them civilians, have been killed in the battered territory and nearly 7,000 wounded. Fifty-six Israeli soldiers have been killed in Gaza clashes and more than 400 wounded. Three civilians have been killed by Palestinian shelling in Israel.
Netanyahu faces intense pressure from abroad to stand his forces down. The United States and the U.N. Security Council have urged an immediate, unconditional ceasefire by both sides in Gaza to allow in humanitarian relief and for further talks on a more lasting cessation of hostilities.
Israel briefly observed a July 15 ceasefire proposed by Egypt, but Hamas continued attacks, saying its conditions had been ignored. Egyptian officials say they put together a revised truce plan this week that had been provisionally accepted by Israel, though Hamas was still undecided.
U.N. Secretary-General Ban Ki-moon strongly condemned on Wednesday the deaths of at least 15 Palestinians among thousands sheltering at a U.N.-run school. The United Nations said its initial assessment was that Israeli artillery shells hit the facility.
The White House on Thursday condemned the incident. "The shelling of a U.N. facility that is housing innocent civilians who are fleeing violence is totally unacceptable and totally indefensible," spokesman Josh Earnest said.
The U.S. Defence Department urged Israel on Thursday to do more to protect civilian life during its military operations.
"The civilian casualties in Gaza have been too high. And it's become clear that the Israelis need to do more to live up to their very high standards - their very high and very public standards - for protecting civilian life," Pentagon spokesman Colonel Steve Warren said at a news briefing.
The United Nations' senior human rights official, Navi Pillay, said Israel had attacked homes, schools, hospitals and U.N. premises in apparent violation of the Geneva Conventions.
Pillay said Israeli actions seemed to be in "deliberate defiance of obligations that international law imposes".
Israel said its forces were attacked by guerrillas near the school in Jabalya in north Gaza and had fired back. In another incident on Wednesday, 17 people were killed in nearby Shejaia by what Palestinian officials said was Israeli shelling of a produce market. Seven more died of their wounds on Thursday.
The Israeli military said it was investigating.
"Such a massacre requires an earthquake-like response," said Hamas spokesman Fawzi Barhoum, whose militants have kept up dozens of daily rocket launches deep into Israel.
The Israelis have kept casualties from the salvoes low, using the Iron Dome air defence system to intercept them and air-raid sirens to send people to shelters.
In Beit Lahiya, another northern Gaza town, Israeli tank shells landed near another U.N.-run school and at least 30 people sheltering inside were wounded by shrapnel and shattered glass, witnesses and hospital officials said.
Rolling Israeli ground assaults on residential areas, preceded by mass warnings to evacuate, have displaced more than 200,000 of Gaza's 1.8 million Palestinians. The tiny territory's infrastructure is in ruins, with power and water outages.
Israel says it is trying to avoid civilian casualties and blames these on Hamas and other groups dug in for urban combat.
Both sides have voiced openness to a truce, but their terms diverge dramatically. Israel wants Gaza stripped of infiltration tunnels and rocket stocks. Hamas rules that out, and seeks an end to a crippling Gaza blockade enforced by Israel and Egypt, which view the Palestinian Islamists as a security threat.
Diplomacy to end the Gaza conflict is further complicated by the fact Israel and the United States shun Hamas as a terrorist group, while the go-betweens - Egypt, Qatar and Turkey - disagree on Gaza policy.
In early 2009, Israel ended a three-week Gaza war with a unilateral ceasefire with Hamas, Islamic Jihad and other smaller militant factions following suit.
Israel has ordered its ground forces to focus on locating and destroying a warren of tunnels through which Hamas has menaced its southern towns and army bases.
Major General Sami Turgeman, chief of Israeli forces in Gaza, said on Wednesday they were "but a few days away from destroying all the attack tunnels".
"Progress has been satisfactory, and we are completing our treatment of the terror tunnels," Defence Minister Moshe Yaalon said on Thursday. "During the fighting, soldiers are finding new tunnel shafts, and they are also being neutralised."
Three Israeli soldiers were killed on Wednesday by a booby trap detonated as they uncovered a tunnel shaft, the army said. Military losses are more than five times those from the last Gaza ground war, in 2008-2009, but Israeli opinion polls show strong public support for fighting on until Hamas is quelled.
Washington has also allowed Israel to tap a local U.S. arms stockpile in the past few weeks to replenish its grenades and mortar rounds, a U.S. defence official said on Thursday.
U.S. Secretary of State John Kerry, who failed in a visit to the region last week to secure a ceasefire, voiced support for Israel's operations against the tunnels.
"No country can sit there and live with tunnels being dug under its border, out of which jump people who are carrying handcuffs and tranquilizer drugs in order to kidnap their citizens and hold them for ransom," Kerry said in an interview broadcast on Thursday by India's NDTV.