Israel's operation against Hamas saw one of its bloodiest days on Saturday, with 46 Palestinians killed in Gaza and two Israeli soldiers and a civilian killed by militant fire.
As Israeli warplanes bombarded Gaza from the air, and ground troops pressed an assault on land, the Palestinian overall death toll on day 12 of Israel's Operation Protective Edge rose to 342, with rights groups warning that a growing number of victims are children.
UN chief Ban Ki-moon was Saturday headed for the region to bolster intense diplomatic efforts aimed at ending the bloodshed in and around Gaza.
Israel meanwhile warned it was ready to intensify its ground assault aimed at destroying a network of cross-border tunnels.
Despite the blistering offensive, Palestinian commandos in central Gaza managed to use tunnels to infiltrate southern Israel in three separate cases, killing two soldiers in one incident with four of their men killed in the attacks.
Also Saturday, an Israeli Bedouin was killed when a rocket hit his encampment in southern Israel in an attack which also wounded four of his family, among them two young children, police said.
The deaths raised to five the total number of Israelis killed since July 8 -- three soldiers and two civilians -- in the deadliest confrontation between Israel and Hamas militants since 2009.
According to army data, 76 rockets and mortars hit Israel on Saturday with another 14 intercepted, bringing the number of projectiles hitting Israel in the past 12 days to 1,321, with 356 intercepted.
Israel's Chief-of-Staff, Lieutenant General Benny Gantz, said the army was "expanding the ground phase of the operation", warning there would be "moments of hardship", alluding to the possibility of further Israeli casualties.
In Gaza, after a relative lull on Friday, violence picked up again, with intensifying tank shelling and air strikes killing 46 people on Saturday.
Among Saturday's dead were two six-year-olds and a toddler, emergency services spokesman Ashraf al-Qudra said.
The increasing number of children killed in the conflict is causing a growing outcry, with a joint statement from the NGOs War Child and Defence for Children International saying more children had been killed than militants.
Figures provided by the UN children's agency, UNICEF, indicate 73 of the victims were under the age of 18.
"Children should be protected from the violence, and they should not be the victims of a conflict for which they have no responsibility," UNICEF's Catherine Weibel told AFP.
The UN agency for Palestinian refugees UNRWA has opened 44 of its schools to shelter those fleeing the most heavily-bombarded areas.
So far, more than 50,000 Gazans have sought sanctuary at UN institutions, the agency said.
Ban was leaving for the Middle East on Saturday to help Israelis and Palestinians "end the violence and find a way forward", the agency said.
In Amman, French Foreign Minister Laurent Fabius said brokering a ceasefire must be the "absolute priority," urging all parties an Egyptian-led effort.
Palestinian president Mahmud Abbas and Hamas political leader Khaled Meshaal will meanwhile meet in Qatar on Sunday to discuss a truce in Gaza, an official close to Abbas said.
An Egyptian-led truce effort collapsed earlier this week after Israel accepted it but Hamas militants continued to fire rockets over the border.
Hamas spokesman Fawzi Barhum told AFP his movement had given "the demands of the resistance to all the parties concerned, including Qatar, Turkey and the Arab League" as well as Abbas and Egypt.
The demands included an end of the "war on the Gaza Strip," a complete lift of the siege on it, opening the Rafah crossing with Egypt, freedom of movement in the border areas, cancelling the buffer zone and expanding the freedom to fish 12 nautical miles from shore.
In addition, Hamas demanded the release of its members who had been freed in the 2011 Shalit deal and recently arrested in an Israeli crackdown on the West Bank.
In northern Israel, the growing violence brought angry protestors onto the streets, where 1,500 Arab Israelis demonstrated in Kafr Kana against Israel's military operation, police said.
In the northern coastal city Haifa some 800 Israelis held a demonstration in favour of Israel expanding its Gaza operation, while 350 Israelis at the same site were protesting against it.
Protests against the Israeli offensive have also sprung up across the world, with thousands joining a pro-Palestinian rally in London, chanting "Israel is a terror state", while demonstrators in Paris clashed with riot police after their own protest was banned.