United Nations Secretary-General Ban Ki-moon has urged Israel and the Palestinians to "stop fighting" and "start talking" to end the conflict in Gaza.
He was speaking in Israel as diplomatic efforts intensified.
More than 600 Palestinians and 30 Israelis have been killed in the past 14 days of fighting, officials say.
Earlier, US Secretary of State John Kerry said a previous Egyptian plan should form the basis of a ceasefire.
Speaking in Egypt, Kerry said the US was concerned about Palestinian casualties, but lent his support to Israel's "appropriate and legitimate" military operation.
He also said the US was sending $47m (£28m) in aid to Gaza "to alleviate the immediate humanitarian crisis".
Kerry is expected to stay in Cairo until at least Wednesday for talks with Egyptian officials and the Arab League chief Nabil al-Arabi.
At a joint news conference with Israeli Prime Minister Benjamin Netanyahu, Mr Ban urged Israel to exercise "maximum restraint", adding that "military action will not increase Israeli security in the longer term".
He called on the Palestinians to pursue a policy of "no violence, recognition of Israel and respect for previous agreements".
Replying to Mr Ban's opening comments, Mr Netanyahu asked: "What grievance can we resolve for Hamas? Their grievance is that we exist."
The latest Palestinian death toll of more than 600 was announced by Gaza's health ministry, which also said that 3,640 people had been injured.
The UN relief agency in Gaza said one of its schools, in which around 300 people had been taking shelter, had been hit by Israeli shelling on Tuesday.
UNRWA says more than 118,300 Palestinians have now taken refuge in its shelters. It says 43% of Gaza has been affected by evacuation warnings or declared no-go zones.
Some 50 Palestinians have been killed here since midnight local time. Health officials told us that doctors tried to rescue the baby of a pregnant woman from Jabaliya who was killed in an air strike, only for the child to die.
Close to the BBC office in Gaza City, body parts could be seen in the rubble of the "Peace Tower" apartment building. Two families - 11 people - were killed overnight.
A distraught man told us how his dead relatives who were staying there had relocated twice first from Beit Hanoun and then Shajaiya, areas that received Israeli military evacuation orders.
At the Rafah border crossing a BBC team was told only two injured people were able to exit to Egypt, leaving a frustrated crowd behind them.
Most ordinary Palestinians are weary and afraid. They sorely want an end to this fighting but many also insist conditions for a ceasefire must be met - including easing the tight border restrictions imposed on Gaza by Israel and Egypt.
(BBC)
