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Israel has warned it could "significantly widen" a Gaza land offensive but was cautioned by its main ally, the United States, about the risks of further escalation as Palestinian civilian deaths mounted.
Palestinian officials said 58 Palestinians, at least 15 of them under the age of 18, have been killed since Israel sent ground forces on Thursday into the densely-populated enclave of 1.8 million Palestinians.
The Israeli military said it killed 17 Palestinian gunmen while another 13 surrendered and were taken for questioning after the infantry and tank assault began in the Islamist Hamas-dominated territory.
One Israeli soldier was killed in an apparent friendly fire incident, the military said, and several other troops were wounded in the ground operations. It said some 150 targets, including 21 concealed rocket launchers and four tunnels, have been attacked.
U.S. President Barack Obama said on Friday he had spoken to Prime Minister Benjamin Netanyahu, underscoring Washington's support for Israel to defend itself but raising concerns about "the risks of further escalation" and additional loss of innocent lives.
"We are hopeful that Israel will continue to approach this process in a way that minimises civilian casualties," Obama told reporters at the White House.
U.N. Secretary-General Ban Ki-moon planned to travel to the Middle East on Saturday in a bid to end the hostilities.
At an emergency session of the U.N. Security Council on Friday, U.N. political affairs chief Jeffrey Feltman condemned rocket fire into Israel but voiced alarm at "Israel's heavy response".
The Israeli land advance followed 10 days of barrages against Gaza from air and sea, hundreds of rockets fired by Hamas into Israel and failed attempts by Egypt, a broker of ceasefires in previous Israeli-Palestinian flare-ups, to secure a truce.
After nightfall on Friday, flares fired by Israeli forces cast an orange glow above the coastal enclave as explosions echoed in what appeared to be intensified Israeli attacks from the air and ground.
Rocket salvoes, many of them intercepted by the Iron Dome anti-missile shield system, continued on Friday against southern Israel and the Tel Aviv metropolitan area, police said, causing no casualties.
"We chose to start this operation after we exhausted other options and reached the conclusion that without it we could pay a much higher price," Netanyahu told reporters before a special cabinet session at Tel Aviv military headquarters. "The main goal is to restore quiet.
"My instructions...to the Israeli army, with the approval of the security cabinet, is to prepare for the possibility of a widening, a significant widening of the ground operation."
He did not say what form a broadened offensive might take. Israel says its forces have focused so far on seeking out tunnels Palestinian militants might use for cross-border raids and moving weaponry.
One such infiltration was narrowly thwarted on Thursday, with the army saying it had repelled 13 Hamas gunmen after they emerged from a tunnel close to an Israeli farming community.
In all, 291 Palestinians - most of them civilians, of whom at least 50 were under the age of 18 - have been killed since fighting began on July 8, Gaza officials said.
There have been two Israeli fatalities - the soldier and a civilian, who was killed by a rocket. More than 100 rocket bursts a day at southern Israel and the heartland Tel Aviv area have sent hundreds of thousands dashing for shelters.
Gaza residents said Israeli forces has moved several hundreds metres (yards) into the north of the enclave and their deployment in the south of the territory was slightly deeper.
Hamas said its men were hitting Israeli tanks with mortar rounds and setting off bombs against troops crossing the sandy frontier under smokescreens.
To back up regular forces, Israel said it was calling up 18,000 military reservists, adding to 30,000 already mobilised. Abu Ubaida, spokesman for Hamas's armed wing, said it had thousands of fighters of its own "waiting to join the battle".
Hamas wants Israel and Egypt, whose military-backed government is at odds with the Palestinian Islamists, to lift border restrictions that have deepened Gaza's economic hardship and unemployment.
Israel briefly halted its Gaza assaults on Tuesday after accepting an Egyptian truce proposal. But Hamas, an offshoot of the outlawed Muslim Brotherhood in Egypt, said the plan failed to address its demands on ending the border blockades and releasing hundreds of its activists in the occupied West Bank activists held by Israel.
A U.S. official said Secretary of State John Kerry had been in regular contact with the foreign minister of the Gulf Arab state of Qatar, which has close links with Hamas, and other leaders "on how to get a ceasefire".
Qatar has suggested it take over as mediator but the U.S. and Israel say it is too close to Hamas to take on that role.
"In all his recent calls, the Secretary has made clear that we support the Egyptian proposal, and that we hope that everyone can get behind it," the official said. "There are no other serious ceasefire proposals being discussed."
Kerry's position was echoed by Amos Gilad, a senior Israeli Defence Ministry official who has held talks with Egypt's military-backed government on Cairo truce plan.
"It is important for Qatar to understand that an alternative initiative would be useless," he said on Israel's Channel 10 TV. "Let's be realistic: who borders Gaza - Qatar or Egypt?"
Egyptian Foreign Minister Sameh Shukri, speaking at a news conference with his French counterpart Laurent Fabius, called on all sides to accept Cairo's ceasefire initiative.
"We are working to find a framework so that both sides agree," Shukri said.
Though they are die-hard enemies, Israel says it does not intend to topple Hamas, the dominant Islamist force in Gaza.
The current conflict - the worst warfare between Israelis and Palestinians in two years - was stoked by the killing of three Israeli teens in the West Bank last month and the death on July 2 of a Palestinian youth in a suspected revenge murder.
Israel last mounted a large-scale invasion of the Gaza Strip during a three-week war in late 2008 and early 2009 that claimed 1,400 Palestinian and 13 Israeli lives.