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, Mr 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".
Mr 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.
At the scene - the BBC's Yolande Knell in Gaza City
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.
The BBC's Chris Morris reports from Jerusalem
The vast majority of the people killed in this conflict have been Palestinian civilians in Gaza. But Israeli military casualties are unexpectedly high - 28 soldiers killed so far.
If anything, this has increased a sense of solidarity. Military service is compulsory for most here, and there is huge sympathy for the armed forces.
One of the soldiers killed in Gaza on Sunday, Sean Carmeli, held joint US-Israeli citizenship and his family lives in the United States.
So the Israeli football team he supported, Maccabi Haifa, appealed on Facebook for fans to attend his funeral, to ensure he was not buried alone. Twenty thousand people turned up.
Plenty of Israelis are uncomfortable with Gaza's high civilian death toll. But a clear majority continues to support a military operation designed to limit Hamas's ability to fire rockets into Israel, and to infiltrate Israeli territory.
The extent of the cross-border tunnel network dug by Hamas has been a big shock for some. And Israelis want the threat removed.
Voices: 'I'm not afraid of being killed'
The majority of Palestinians killed have been civilians, including dozens of children, according to the UN.
The IDF also says it has killed at least 170 militants. Israel says 28 of its soldiers and two Israeli civilians have died over the past two weeks.
Early on Tuesday, Israeli air strikes destroyed several mosques and targeted a stadium and the home of the late leader of Hamas's military wing.
Israel launched its ground operation in Gaza after days of air strikes, following rocket fire by militants into Israeli towns.
It says the move is necessary to target Hamas' network of tunnels, which have been used by militants to get into Israel and carry out attacks.
Also on Tuesday, the US Federal Aviation Administration (FAA) suspended all flights into Israel's Ben Gurion Airport for 24 hours, citing security fears.
There were reports that several European airlines were following suit, including Lufthansa, Air France and KLM.
Meanwhile, Israel says a soldier hit in a Hamas attack in Gaza on Sunday is missing.
Sgt Oron Shaul, 21, was the last of seven soldiers reported killed in a single incident in Shejaiya, near Gaza City, on Sunday. Local media say he is presumed dead.
Hamas said on Sunday evening that it had captured an Israeli soldier, but Israel denied the claim.