The UN Security Council has called for an immediate ceasefire in Gaza after holding an emergency closed-door meeting on the crisis.
The urgent talks came after Ban Ki-moon described Israel's shelling of a Gaza City suburb as "an atrocious action".
Sunday was the deadliest day of fighting, with 13 Israeli soldiers and more than 100 Palestinians killed.
US Secretary of State John Kerry is due in Cairo on Monday to discuss the crisis with Egyptian leaders.
Eugene Gasana, Rwanda's ambassador to the UN, said the Security Council members had expressed concern at the escalation of violence after a "sobering session".
He also said members had expressed "serious concern at the growing number of casualties" and called for "the respect of international humanitarian law, including protection of civilians".
Israel launched a ground offensive last week, saying the operation was crucial to weakening Hamas 
The number of Palestinians killed during the offensive rose sharply at the weekend and is nearing 500 Diplomatic efforts to resolve the conflict were stepped up as the number of Palestinians killed since the start of Israel's offensive two weeks ago neared 500.
'A massacre'More than 60 Palestinians alone were killed during heavy shelling in the Shejaiya district of Gaza, with Palestinian President Mahmoud Abbas calling it "a massacre".
He called for urgent talks, saying the "situation is intolerable" in Gaza and describing the Israeli attacks as "crimes against humanity."
Israeli Ambassador Ron Prosor said Hamas must be "demilitarised"
Palestinian ambassador Riyad Mansour said the UN must take responsibility
Israeli Prime Minister Benjamin Netanyahu vowed to continue operations "as much as we need to" despite the number of Israeli soldiers killed rising to 18 at the weekend.
Two of the soldiers killed were American citizens, US state department spokesperson Jen Psaki said.
Sunday's death toll for Israel's military is higher than that sustained during the entire three-week duration of Operation Cast Lead in 2008-2009, the last time Israel sent troops into Gaza.
The deaths of so many soldiers on a single day will shock Israeli society, the BBC's Chris Morris reports from southern Israel.
Prime Minister Netanyahu vowed to continue operations despite the loss of 13 soldiers on Sunday 
There were celebrations in Gaza and the West Bank after Hamas claimed it had captured an IDF soldier Hamas said on Sunday evening that it had captured a member of the Israel Defense Forces (IDF), prompting celebrations on the streets of Gaza and West Bank.
A spokeswoman for the Israeli military said they were investigating but Israel's UN ambassador Ron Prosor denied the claim.
"There's no kidnapped Israeli soldier and those rumours are untrue," Mr Prosor said.
The UN says 83,695 people have now been displaced in Gaza and that the figure is "rising all the time".
John Simpson reports: ''Israel isn't used to losing soldiers on such a scale''
The BBC's Lyse Doucet says families are fleeing Shejaiya, east of Gaza City
The BBC's Yolande Knell, in Gaza City, says there have been scenes of panic in Shejaiya, with thousands of residents fleeing.
In an interview with BBC Arabic, Mr Netanyahu called Shejaiya a "terror stronghold" and a centre for rocket attacks on Israel.
Mr Netanyahu said Israeli troops had no choice but to enter densely populated areas and that they had asked civilians to leave.
Israeli residents in the town of Sderot gathered on a hillside to watch the ongoing fighting in Gaza The death toll in Gaza rose sharply over the weekend and further Israeli bombardment early on Monday killed another 38 people, according to health officials.
The total number of Palestinians killed now stands at 476, according to the AFP news agency, with the number of wounded at more than 3,000.
The majority of those killed are civilians, the UN says.
The Israel Defense Forces (IDF) sent ground troops into Gaza on Thursday after days of heavy air and naval barrages failed to stop rocket fire from Gaza.
Two Israeli civilians have died since the offensive began on 8 July.
Israel says the ground operation is necessary to target Hamas tunnel networks, which it says it could not do from the air alone.
Are you in the area affected? Are you or is someone you know affected by the situation? Email your comments to haveyoursay@bbc.co.uk using the subject 'Gaza'.
UN calls for Gaza ceasefire
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