Israeli soldiers in tanks and bulldozers dug in across a mile-wide strip of Gaza's eastern frontier on Saturday as Palestinian officials said military strikes had killed more than 300 people, most of them civilians.
Israel launched a ground offensive on Thursday after 10 days of air and naval barrages
The military said its engineers were concentrating on a buffer-zone 2.5 km (1.5 mile) wide and were looking to destroy tunnels and concealed rocket launch pads dug by Gaza's dominant Hamas Islamists after the last big flare-up of violence in 2012.
Hamas said its fighters used one such tunnel to slip into Israel on Saturday, inflicting casualties. The Israeli military confirmed the incident near central Gaza, saying it killed one militant, repelled the rest, and that two soldiers were wounded.
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Palestinian militants also fired at least 18 rockets into Israel on Saturday, killing a man and wounding four people, including two children, in the southern town of Dimona, police said.
Gaza officials said that at least 318 Palestinians, including 70 children, have been killed in the 12-day conflict. On Israel's side, a soldier and two civilians have been killed.
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Hostilities had escalated following the killing last month of three Jewish seminary students that Israel blames on Hamas. Hamas neither confirmed nor denied involvement. The apparent revenge murder of a Palestinian youth in Jerusalem, for which Israel charged three Jews, further fuelled tensions.
Military spokesman, Lieutenant-Colonel Peter Lerner, said 13 tunnels, at least one of them 30 metres (90 feet) deep, and 95 rocket launchers were found and destroyed in the Gaza sweep.
Searches were continuing in what he described as an open-ended mission that had "severely impeded Hamas capabilities".
Responding to a Reuters inquiry, the military acknowledged that there was a de facto buffer zone in eastern Gaza but said other Israeli operations continued. Brigadier-General Moti Almoz, chief military spokesman, signalled that the forces conducting the unearthing mission would not stay permanently.
"I can't promise that when we leave the territory we will have exposed all of the tunnels," he told Israel's Army Radio.
Gaza medical officials said attacks overnight from Israel killed 26 Palestinians, mostly civilians, in the northern towns of Beit Hanoun and Beit Lahiya and in Khan Younis in the south.
The military had no immediate word on the Beit Lahiya and Khan Younis incidents, though it confirmed carrying out 37 strikes. It said troops raiding a house in Beit Lahiya killed a gunman after he wounded three soldiers. The Palestinian faction PRC said it ambushed the Israeli troops in Beit Lahiya.
Israel says more than 1,500 rockets have been fired at its towns and cities during this month's fighting. The death toll has been kept low due to the rockets' inaccuracy, an extensive Israeli network of air raid sirens and shelters and its anti-missile shield Iron Dome's 90 percent success rate.
The escalation of hostilities, and its toll on Gaza's 1.8 million Palestinians as well as on Israelis jarred by rockets that have reached Tel Aviv and beyond, have spurred so-far fruitless truce bids by Western powers and regional go-betweens.
"There will be no truce without an end to the war that the Occupation (Israel) began, a lifting of the blockade and a halt to all violations and killings in Gaza and the West Bank," Hamas spokesman Sami Abu Zuhri said.
Egypt has no plans to revise its ceasefire proposal, which Hamas has rejected, Cairo's foreign minister said on Saturday.
U.N. Secretary-General Ban Ki-moon planned to travel to the Israel and the Palestinian territories this weekend. At an emergency session of the U.N. Security Council on Friday, U.N. political affairs chief Jeffrey Feltman condemned the rockets from Gaza but voiced alarm at "Israel's heavy response".
The United Nations said that more than 50,000 Palestinians have taken refuge from the Israeli attacks in its Gaza shelters.
Palestinian officials said 90 percent of Gaza's electricity had been cut by Israel. The Israeli energy ministry had no immediate response. On Sunday, it said a Palestinian rocket had crippled a power line to Gaza from Israel and it would not endanger engineers by sending them to conduct repairs.
Hamas, Gaza's dominant Islamist group, refuses to hold fire unless embargoes by Israel and neighbouring Egypt are eased and other demands are met. The Israelis say they are ready to step up their Gaza assault, though they do not aim to topple Hamas.
U.S.-backed Palestinian President Mahmoud Abbas, who entered a power-share deal with his Islamist rivals in April, has been shuttling between Egypt and Turkey in search of a breakthrough.
Turkey serving as an intermediary looked unlikely, however, after Israel pared down its diplomatic missions in Ankara and Istanbul this week following sometimes violent pro-Palestinian street protests and what it deemed "incitement" against its by the Islamist-rooted Turkish Prime Minister Tayyip Erdogan.
On Saturday, the Foreign Ministry in Jerusalem advised Israelis to avoid "non-essential" travel to former ally Turkey.
France has also mooted mediation by Qatar, which has helped fund Gaza projects in the past, but Israel is cool to the idea.
The Israelis prefer Egyptian intercession. Yet with Egypt having cracked down on its Muslim Brotherhood - Hamas's ideological kind - and viewing Hamas as a security threat, Cairo's clout with the Palestinian Islamists is in doubt.