The Israeli military has launched air strikes over the northern Gaza Strip after people in the town of Beit Lahiya were told to leave their homes.
Israel had dropped leaflets urging local residents to leave the area, in advance of an expected wider attack on Sunday.
The small Palestinian territory has been struck by Israeli fire power for six days now and the number of deaths keeps rising.
At least 167 people have been killed since the attacks began, Gaza's Health Ministry says. Of those, at least 29 are children below the age of 16, while 19 of the casualties have been women.
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Israeli forces also shelled southern Lebanon after a cross-border rocket attack, both sides said.
A spokeswoman for Israel's army said it "immediately responded with artillery fire towards the source of the fire" from Lebanon on Monday, where security sources confirmed the Israeli shelling.
Earlier in the day, Israeli soldiers clashed with Hamas fighters in the first reported ground incursion in Gaza, after a night of violence in which 18 members of the same family were killed.
The Israeli army said at least four soldiers were "lightly injured" on Sunday when they attacked a site in northern Gaza the army said was being used to launch long-range rockets.
"During the mission a gunfight broke out, started by some terrorists operating at the site, during which four Israeli soldiers were lightly wounded," the spokesman said.
The Qassam Brigades, Hamas' armed-wing, confirmed the exchange of gunfire "between our fighters and soldiers of the Zionist navy which tried to penetrate the zone of Sudanyia" in northwest Gaza.
Hamas said its fighters had fired at the Israeli force offshore, preventing them from landing.
The early morning incursion followed the deadliest night of Israeli bombing since it launched its campaign on Tuesday.
Eighteen people, from the same extended family, were killed in the deadliest attack since the bombardment of the Palestinian territory began on Tuesday, when Israeli forces targeted the home of Tayseer al-Batsh, Gaza police chief, in the Toufah area of Gaza City.
Ashraf al-Qedra, a spokesman for the Gaza Health Ministry, told Al Jazeera that the house, located near a mosque in Toufah, was hit after Ramadan prayers.
Adnan Abu Hassna, a spokesman for the UN agency in charge of aiding Palestinian refugees, said eight schools were opened as temporary shelters, and about 4,000 people had moved in.
Foreign-passport holders leaving
On Sunday, Palestinians with foreign passports began leaving Gaza through the Erez border crossing.
Israel says 800 Palestinians living in Gaza have passports from countries including Australia, the UK and the US.
Against this backdrop, Palestinian President Mahmoud Abbas called on the international community to protect Gaza.
"Israel went deeper in everything and its offensive on the Palestinian nation should be stopped," he said.
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Israel says its bombardment is to end rocket fire by Palestinian fighters into Israeli cities. The UN on Saturday said that three-quarters of those killed in Gaza were civilians.
The Israeli army said late on Saturday that rockets fired from Gaza had hit Hebron and Bethlehem.
No deaths or injuries was reported. Palestinians in the two Occupied West Bank cities protested against Israeli troops on Sunday morning.
More than 500 missiles have struck Israel during the conflict, but none have resulted in Israeli deaths.
Israel has launched more than 1,400 air strikes since the offensive began.
An Israeli air raid on Saturday hit a centre for the disabled in Gaza, killing three patients and a nurse.
The UN Security Council called for a cessation of hostilities and top diplomats from the UK, France, Germany and the US are due to meet later on Sunday to discuss the need for a ceasefire.
However, Benjamin Netanyahu, Israel's prime minister, said on Sunday the military campaign could take a long time.
Source: Al Jazeera and agencies