The UN Security Council has called for an immediate ceasefire between Israel and Palestinian militants in Gaza.
It comes as US Secretary of State John Kerry heads to Cairo for talks on the crisis amid a mounting death toll.
More than 500 Palestinians, mainly civilians, have been killed since the Israeli offensive began 13 days ago, Gaza's health ministry says.
Twenty Israelis - 18 of them soldiers - have died, Israel says, as it seeks to end rocket fire from Gaza.
Sunday was the deadliest day since the start of Israel's offensive, with 13 Israeli soldiers and more than 100 Palestinians killed.
Israel says it has killed at least 120 militants since Thursday night when it launched a ground offensive, the second phase of a military operation that began on 8 July.
In other developments:
- Overnight air strikes in southern Gaza kill more than 30 members of two families in Khan Younis and Rafah, local officials say
- Artillery fire and air strikes continue to the east of Gaza City, with Israeli aircraft seen over Shejaiya district for a second day, and the Maghazi neighbourhood
- Ten Hamas militants die after using tunnels in the northern Gaza Strip to infiltrate Israel near the town of Sderot, Israel says.
Sunday's late-night UN Security Council session was convened at the request of Jordan, which is understood to have proposed a strongly worded draft resolution for consideration.
However, the 15-member council instead issued a statement to the media, with Rwanda's UN ambassador calling for "an immediate cessation of hostilities".
Israel urged residents to flee before attacking Shejaiya
Eugene Gasana said members voiced alarm at the escalation of violence during a "sobering session".
UN Secretary General Ban Ki-moon had earlier spoken out on the situation, describing an Israeli assault on the densely populated Shejaiya neighbourhood of Gaza as "an atrocious action".
More than 60 Palestinians alone were killed during heavy shelling in Shejaiya, in what Palestinian President Mahmoud Abbas called "a massacre".
He called for urgent talks, saying the "situation is intolerable" in Gaza and describing the Israeli attacks as "crimes against humanity."
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 Israel's last ground offensive in Gaza in 2008-2009.
The deaths of so many soldiers on a single day will shock Israeli society, the BBC's Chris Morris reports from southern Israel.
Hamas said on Sunday evening that it had captured an Israeli soldier, prompting celebrations on the streets of Gaza and West Bank.
However Israel's UN ambassador Ron Prosor denied the claim, saying "those rumours are untrue".
The UN says 83,695 people have now been displaced in Gaza and that the figure is "rising all the time".
There were scenes of panic in Shejaiya, with thousands of residents fleeing.
Analysis: Jonathan Marcus, BBC defence correspondent
The fact that the battle has moved into a heavily populated urban area means that the civilian death toll will rise markedly. With it will come added pressure from outside to end the operation once and for all.
Hamas's infiltration tunnels prompted the Israeli movement on the ground. Many civilians may have fled but clearly others remained. Now the fighting is close-up and bitter and it's taking a toll on the Israelis as well.
This may well be exactly what Hamas military commanders wanted: to draw the Israeli forces into a close urban environment, a difficult battleground for any modern army.
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.
Israel sent ground troops into Gaza after days of heavy air and naval barrages failed to stop rocket fire.
Israel says the ground operation is necessary to target Hamas' network of tunnels, which it says have been used by militants to infiltrate Israel and carry out attacks.