* Netanyahu presses assault, sends envoys to Cairo
* U.N. outraged at refugee deaths at Gaza shelter
* Palestinian deaths exceed 1,360; 56 soldiers and three civilians on Israeli side
GAZA/JERUSALEM, July 31 (Reuters) - Israel pressed ahead with its Gaza offensive saying it was days from achieving its core goal of destroying all Islamist guerrilla cross-border attack tunnels, but a soaring Palestinian civilian toll has triggered international alarm.
Prime Minister Benjamin Netanyahu's security cabinet on Wednesday approved continuing the assault launched on July 8 in response to a surge of rocket attacks by Gaza's dominant Hamas Islamists. Israel also sent a delegation to Egypt, which has been trying, with Washington's blessing, to broker a ceasefire.
A military source said some 16,000 reservists were being called up at short notice in the coming hours to relieve a similar number who would be stood down.
Gaza officials say at least 1,361 Palestinians, most of them civilians, have been killed in the battered enclave 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 in Palestinian shelling in Israel.
U.N. Secretary-General Ban Ki-moon was incensed on Wednesday at the deaths of at least 15 Palestinians among thousands sheltering at a school whose U.N. administrator said appeared to have been hit by Israeli artillery.
"It is outrageous. It is unjustifiable. And it demands accountability and justice," Ban said.
Israel said its forces were attacked by guerrillas near the school, in northern Jabalya, and had fired back. It did not comment immediately on another incident, in nearby Shejaia, in which Palestinian officials said 17 people were killed by Israeli shelling near a produce market.
"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 with nine Iron Dome interceptor batteries and air-raid sirens that send people to shelters.
Rolling Israeli ground assaults on residential areas, prefaced 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.
The negotiations are 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 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.
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.
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.
Separately, the Pentagon said it had allowed Israel to stock up on grenades and mortar rounds from a U.S. munitions store located in Israel as part of bilateral emergency preparedness arrangement.
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.
However, an Israeli security cabinet minister, Gilad Erdan, denied on Wednesday that his side was suing for a truce.
"We are not looking for a ceasefire, though of course military manoeuvres are supposed to be followed by diplomatic manoeuvres," Erdan said. "But a ceasefire must fulfil Israel's terms, a long-term calm and the demilitarization of Gaza." (Writing by Dan Williams; Editing by Michael Perry and Paul Tait)