And the overall Israeli death toll rose to five following violence in which two soldiers and a civilian were killed, the army and police said.
The latest incident in Gaza saw one man killed in an air strike on the northern town of Jabaliya shortly after two were killed in a strike near Deir al-Balah in central Gaza, emergency services spokesman Ashraf al-Qudra said.
WATCH: Israeli troops push deeper into Gaza to widen ground offensive
And another two people were killed in Zeitun, east of Gaza City, raising the number of Palestinians killed on Saturday to 46.
In southern Israel, two soldiers were killed when a group of Gaza militants got under the border fence and fired machineguns and an anti-tank missile at an army patrol.
Troops returned fire killing one of the militants in an attack claimed by Hamas.
Also in the south, an Israeli Bedouin man was killed and four family members wounded, two of them children, when a rocket hit their desert encampment not far from Israel's nuclear reactor in Dimona, police said.
Read: Israeli border shelling sends refugees pouring inland
Read: Key demands, issues in Israel-Gaza cease-fire
Their deaths raised to five the number of Israelis killed since the conflict began on July 8, including a soldier who was reportedly killed by friendly fire.
Among those killed in Gaza were five members of the same family, including a 6-year-old and a 2-year-old, who died in a strike on a house in the northern town of Beit Hanun, Qudra said.
Earlier, Qudra also reported five bodies had been pulled from a home hit by an Israeli air strike in Khan Yunis.
So far, more than 2,385 Palestinians have been wounded in the biggest confrontation in and around Gaza since Operation Cast Lead, a bloody 22-day offensive which ended in January 2009.
Palestinian siblings Maria Abdel Aal and Misk cry as the body of their relative Bashir Abdel Aal, killed in an overnight Israeli missile strike in Rafah, southern Gaza Strip, is carried away from the family house, during his funeral. (AP photo)
Israel sent ground forces into Hamas-controlled Gaza on Thursday after 10 days of air and naval barrages failed to stop rocket fire from the Palestinian territory.
Diplomatic efforts to secure a ceasefire involving, amongst others, Egypt, Qatar, France and the United Nations, have failed to make headway. Hamas rejected an initial attempt by Cairo last week to end the fighting.
The sound of explosions rocked Gaza through the day, while sirens repeatedly sounded in towns and cities in southern and central Israel, warning of approaching missiles.
Israeli bulldozers and engineers worked along a mile-wide strip of Gaza's eastern frontier, uncovering 13 tunnels, at least one of them 30 metres (90 feet) deep, military spokesman Lieutenant-Colonel Peter Lerner said.
About 95 rocket launchers were also found and destroyed in the sweep, he added.
Searches were continuing on what he described as an open-ended mission that had "severely impeded Hamas capabilities".
Hamas says it is continuously replenishing its stock of weapons and is ready for a prolonged conflict.
Read: In Gaza, whatever the target, children often the victim of conflict
The Israeli death toll has been kept low due to the rockets' relative inaccuracy, a network of air raid sirens and shelters and the Iron Dome rocket interceptor's 90% success rate.
The Israeli military urged Palestinians to flee an ever-growing area of Gaza ahead of further military action in the Mediterranean enclave. Locals say about half of the territory's 1.8-million population have been told to move.
An Israeli soldier sits on top of his tank across the northern Gaza Strip. Israel intensified its land offensive in Gaza with artillery, tanks and gunboats. (Reuters photo)
With both the Israeli and Egyptian borders sealed off, Gazans say they have few places to escape to.
The largest United Nations agency in Gaza, UNRWA, said about 61,500 people had sought refugee in its buildings, mainly schools - more than in any previous conflict there between Israel and Islamist militants.
UN secretary-general Ban Ki-moon plans to travel to the region this weekend as part of a growing international efforts to end hostilities, while French foreign minister Laurent Fabius met officials in both Egypt and Jordan to discuss the crisis.
"Our absolute priority is to have a ceasefire. Egypt has put forward a good initiative," Fabius said in Jordan, before heading to Israel for more talks.
However, Egypt said on Saturday it had no plans to revise the ceasefire proposal, which Hamas has already rejected.
Read: Gaza night sky lit up with explosions
Pro-Palestinian protesters took to the streets of numerous European cities, including London and Paris, to demand an immediate end to the conflict.
Overnight Israeli air attacks. AFP
"There will be no truce without an end to the war that the Occupation (Israel) began, a lifting of the blockade and a halt to all violations and killings in Gaza and the West Bank," Hamas spokesman Sami Abu Zuhri said in Gaza.
'Israel more barbaric than Hitler'
Turkish Prime Minister Recep Tayyip Erdogan has accused Israel of "barbarism that surpasses Hitler" during its ground invasion of Gaza.
Erdogan accused Israel of using disproportionate force in Gaza and said the operation there has derailed efforts to normalize Turkish-Israeli ties. Those soured after Israel's 2010 raid on an aid ship which killed eight Turks and a Turkish-American.
Erdogan spoke in a campaign speech Saturday in the Black Sea port city of Ordu. He is running for the presidency in elections next month.
He has been speaking out strongly against Israel during its offensive against Hamas militants in Gaza, which has killed more than 300 Palestinians.
Hundreds have also staged protests in recent days outside Israeli diplomatic mission in Ankara and Istanbul and more were scheduled for later Saturday.
(With inputs from Reuters, AP and AFP)
Full coverage: Gaza under attack