Israeli air strikes killed 20 people in Gaza Saturday, taking the death toll to more than 300, as UN chief Ban Ki-moon headed to the region to bolster truce efforts.
The new peace push came as Israel stood poised to intensify a ground operation inside the besieged Palestinian territory aimed at stemming rocket fire by militants on day 12 of its bloodiest conflict since 2009.
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."
He added that Washington was "hopeful" that 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.
There have been two Israeli deaths so far, one a civilian and one a soldier killed by friendly fire.
Israel has said the aim of the ground operation 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 Saturday that during the past 24 hours the military had seized 13 tunnels into Israel.
In the face of Israel's land, sea and air offensive, Islamist movement Hamas, which is the dominant power in Gaza, has remained defiant as Palestinian president Mahmud Abbas travelled to Egypt and Turkey for truce talks.
An early morning air strike outside a mosque in the southern city of Khan Yunis killed seven people on Saturday, including a woman, emergency services spokesman Ashraf al-Qudra said.
Later raids killed another 13, bringing the death toll so far to 316 Palestinians and two Israelis.
Some 2,250 Palestinians and several Israelis have been wounded.
The UN said Secretary General Ban Ki-moon would leave for the region Saturday in a bid to end the violence.
Ban would help Israelis and Palestinians "in coordination with regional and international actors, end the violence and find a way forward," under secretary general for political affairs Jeffrey Feltman told the Security Council.
- Naming the dead -
The two sides' UN ambassadors traded blame for the violence, with Israel's Ron Prosor insisting no other country would "tolerate... terrorist" rocket fire at its citizens.
Palestinian ambassador Riyad Mansour read aloud the names of the Palestinian dead, including women and children, to the Security Council, and at one point appeared close to tears.
Israeli Prime Minister Benjamin Netanyahu said he had ordered the military to be ready for "a significant broadening of the ground activity."
He then convened his security cabinet to discuss a possible expansion of the campaign, which began on July 8.
Netanyahu said the ground operation was necessary to deal with the tunnels, but admitted there was "no guarantee of 100 percent success."
In Gaza, after a relative lull Friday, violence picked up again in the evening, with intensifying tank shelling and air strikes killing more than a dozen people.
Among them were eight members of a single family, including four children, killed by tank fire on their home in northern Gaza, Qudra said.
The UN agency for Palestinian refugees UNRWA has opened 34 of its schools to shelter those fleeing their homes.
It said there were 47,000 Gazans seeking sanctuary so far.
- Aid agencies gearing up -
The World Food Programme said it had already distributed emergency food rations and food vouchers to more than 20,000 displaced people.
It said it was gearing up for a huge increase in the coming days and hoping to reach 85,000 people with food distributions.
Gaza was also struggling with a 70 percent power outage after electricity lines from Israel were damaged, officials said.
Israel pulled out of Gaza in 2005. Hamas drove out loyalists of Abbas two years later but to the dismay of Israel reconciled with the Palestinian president after US-brokered Middle East peace talks collapsed earlier this year.
French Foreign Minister Laurent Fabius said Abbas had urged Paris to ask Hamas allies Qatar and Turkey to pressure the Islamists into accepting a ceasefire.
Hamas has rejected Egyptian proposals for a truce, demanding an easing of a harsh Gaza blockade imposed by Israel in 2006 and the release of Palestinian prisoners.