The new peace effort came as eight members of a single family were killed in Israeli tank fire in northern Gaza, after Israel warned it was poised to broaden its ground operations.
Earlier, US President Barack Obama said he had telephoned Israeli Prime Minister Benjamin Netanyahu to voice concerns about the crisis and Palestinian president Mahmud Abbas met foreign leaders for talks.
In the face of Israel's land, sea and air offensive, the Islamist movement Hamas remained defiant and warned the Jewish state it would "drown in the swamp of Gaza."
And battles continued early today morning, with the army saying a firefight had caused "several injuries" to soldiers.
The UN said Secretary General Ban Ki-moon would fly to the region today in a bid to end the violence.
"The secretary general... will leave for the region tomorrow to express solidarity with the Israelis and Palestinians," under secretary general for political affairs Jeffrey Feltman told emergency talks at the Security Council.
He said Ban would help Israelis and Palestinians "in coordination with regional and international actors, end the violence and find a way forward."
But 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 Palestinian dead, including women and children to the Security Council, and at one point appeared close to tears.
Israel's ground incursion, launched on the tenth day of an operation to stamp out rocket fire from Gaza, has killed dozens and forced thousands of people to flee. The UN agency for Palestinian refugees UNRWA has opened 34 of its schools to shelter those fleeing.
It said the number of Gazans seeking sanctuary with the agency had more than doubled in one day from 22,000 to more than 47,000.
Yesterday, 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 with the aim of stamping out cross-border rocket fire.
Israel has authorized the enlistment of 53,000 reserve troops, the army said.