Israeli air strikes have pounded Gaza, taking the death toll from a 12-day bombardment to 333, as UN chief Ban Ki-moon heads to the region to join truce efforts
His peace push comes with Israel poised to intensify a ground operation inside the besieged Palestinian territory it says is necessary to stop militants tunnelling into the Jewish state.
Despite the pounding, Palestinian commandos succeeded on Saturday in infiltrating Israel, sparking a deadly skirmish with an army patrol, as Gaza's bloodiest conflict since 2009 showed no let-up.
The United States urged its Israeli ally to do more to limit the high civilian death toll from the operation while supporting the Jewish state's right to defend itself.
President Barack Obama said Washington was "deeply concerned about the risks of further escalation and the loss of more innocent life".
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He added that Washington was "hopeful" Israel would operate "in a way that minimises civilian casualties".
But Israeli army chief Lieutenant General Benny Gantz, said the army was "expanding the ground phase of the operation".
"There will be moments of hardship," he warned in a briefing to the military, anticipating further Israeli casualties.
Troops killed a Palestinian militant who tunnelled into southern Israel but others managed to withdraw back into Gaza, an army statement said.
"Several terrorists infiltrated Israel through a tunnel from the central Gaza Strip," it said, adding that they fired a machine gun and anti-tank missile at an army patrol.
Troops "returned fire, killing a terrorist and forcing the rest back into Gaza."
Hamas's military wing, the Ezzedine Al-Qassam Brigades, said its fighters had carried out the raid.
In a separate incident, the army said, militants had strapped explosives on to a donkey in an attempt to attack troops.
"Yesterday (Friday) evening, there was at least one such attempt, in which a donkey suspiciously began to approach forces," it said.
"The forces engaged the donkey and it exploded at a safe distance."
There have been three Israeli deaths so far since the July 8 start of the Operation Protective Edge campaign to stamp out rocket fire from Gaza.
A Bedouin was killed on Friday and four of his family wounded - including two young children - when a rocket hit their desert campsite near Israel's Dimona nuclear reactor, police said.
Another civilian died on Tuesday when a mortar round exploded in Israel and a soldier was killed by friendly fire inside Gaza on Friday.
Israel has said the aim of the ground operation launched on Thursday night is to destroy Hamas's network of tunnels which are used for cross-border attacks on southern Israel.
Military spokesman Lieutenant General Peter Lerner told journalists on Saturday that during the past 24 hours the military had seized 13 tunnels into Israel.
The UN said Ban would leave for the region on Saturday to help Israelis and Palestinians "end the violence and find a way forward", under secretary general for political affairs Jeffrey Feltman told the Security Council.
In Gaza, after a relative lull on Friday, violence picked up again in the evening, with intensifying tank shelling and air strikes killing more than a dozen people.
A six-year-old child and five members of a single family, including girls aged six and two, were those killed on Saturday, emergency services spokesman Ashraf al-Qudra said.
