* Tunnel destruction a main goal of Israeli ground offensive
* U.N. outraged at refugee deaths at Gaza shelter
* Palestinian deaths exceed 1,400; 56 soldiers and 3 civilians on Israeli side (Adds Pentagon remarks)
By Nidal al-Mughrabi and Jeffrey Heller
GAZA/JERUSALEM, July 31 (Reuters) - Israeli Prime Minister Benjamin Netanyahu, facing international alarm over a rising civilian death toll in Gaza, said on Thursday he would not accept any ceasefire that stopped Israel completing the destruction of militants' infiltration tunnels.
The Israeli military estimated on Wednesday that accomplishing that task, already into its fourth week, would take several more days.
"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 a ground campaign in the Hamas Islamist-dominated Gaza Strip, the Israeli military said it had called up an additional 16,000 reservists. A military source said they would relieve a similar number of reserve soldiers being stood down.
Fighting, however, appeared less ferocious than on previous days this week - more than 100 were killed on Wednesday alone.
Gaza health officials said 19 Palestinians were killed in Israeli assaults on Thursday, which included an air strike on a van in the heart of Gaza City, which killed two people.
The Israeli military said more than 60 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.
Hamas said it fired one rocket at Tel Aviv, which the military said was intercepted.
Netanyahu's security cabinet on Wednesday approved continuing operations launched on July 8 in response to a surge of cross-border rocket attacks. Israel also sent a delegation to Egypt, which has been trying, with U.S. blessing, to broker a ceasefire.
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. defense 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.
Gaza officials say at least 1,410 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.
The Pentagon called on Israel on Thursday to do more to protect civilian life during its military operations in Gaza.
"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.
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 United Nations' senior human rights official, Navi Pillay, said on Thursday that Israel has attacked homes, schools, hospitals, and U.N. premises in apparent violation of the Geneva Conventions.
Pillay said Israel's 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 northern Jabalya 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 group has kept up dozens of daily rocket launches deep into Israel. The Israelis have kept casualties from the salvoes low, using the Iron Dome air defense system to intercept them and air-raid sirens to send people to shelters.
In the northern Gaza town of Beit Lahiya, 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 Palestinian factions 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.
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". The army said 32 of the secret passages had been found so far and half of them blown up.
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.
Israel in early 2009 ended a three-week Gaza war with a unilateral truce with Hamas, Islamic Jihad and other smaller militant factions following suit.
In the absence of a deal, 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.
"Progress has been satisfactory, and we are completing our treatment of the terror tunnels," Defense Minister Moshe Yaalon said on Thursday. "During the fighting, soldiers are finding new tunnel shafts, and they are also being neutralized."
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.
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 durable cessation of hostilities.
On Wednesday, the White House voiced worry at the deaths in Jabalya and other U.N.-run shelters shelled during the clashes.
"We are extremely concerned that thousands of internally displaced Palestinians who have been called on by the Israeli military to evacuate their homes are not safe in U.N.-designated shelters in Gaza," said National Security Council spokeswoman Bernadette Meehan.
"We also condemn those responsible for hiding weapons in United Nations facilities in Gaza," she said, referring to three cases in which the UNRWA aid agency reported rockets found at its schools.
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. (Additional reporting by Maayan Lubell, Ori Lewis and Dan Williams in Jerusalem; Writing by Jeffrey Heller; Editing by Will Waterman and Peter Graff)