With diplomatic efforts to secure a ceasefire gathering pace, US President Barack Obama said he had telephoned Israeli Prime Minister Benjamin Netanyahu to voice concerns about the crisis.
And Abbas reached out for French help to lobby Hamas allies Qatar and Turkey to pressure the Islamists into accepting a truce during talks in Cairo with foreign minister Laurent Fabius.
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)
In the face of Israel's land, sea and air offensive, the Islamist movement Hamas remained defiant and warned the Jewish state it would "drown in the swamp of Gaza"
As Gaza residents spoke of a night of terror, with gunbattles in the south and all-night shelling in the north, Netanyahu said he had ordered the military to ready for "the possibility of a significant broadening of the ground activity."
Immediately afterwards, he convened his security cabinet to discuss plans for a possible expansion of the campaign, which began on July 8 with the aim of stamping out cross-border rocket fire.
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The ground operation, which began in the Gaza periphery at around 20:00 GMT on Thursday, sent thousands of people fleeing west to escape the fighting, with a UN agency saying the numbers of displaced had almost doubled overnight.
"The number of people coming to UNRWA seeking sanctuary from the fighting in Gaza has nearly doubled today. It has risen from 22,000 to over 40,000," said Chris Gunness, a spokesman for the UN agency for Palestinian refugees, saying they were staying in 34 of the agency's schools.
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By mid-morning Friday, the road between Gaza City and Khan Yunis was deserted with only a single minibus, packed with passengers, careering south, its windows covered with makeshift white flags, an AFP correspondent said.
During Friday prayers, imams at Gaza's 1,400 mosques relayed a single message to the faithful: "Be patient and strong, victory will come."
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But it was little comfort for those on the ground with hospitals overwhelmed by a flood of patients.
"The situation is very, very difficult," said doctor Kamel Zaqzuq at Nasser hospital in Khan Yunis. "At night, it's one constant emergency."
With food supplies running desperately low, the World Food Programme said it had already distributed emergency food rations and food vouchers to more than 20,000 displaced people since the conflict erupted on July 8.
But with the ground operation, it was gearing up for a huge increase in the coming days, spokeswoman Elisabeth Byrs told reporters in Geneva.
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"In the next few days, WFP hopes to reach 85,000 people with food distributions," she said.
Gaza was also struggling with a 70% power outage after electricity lines from Israel were damaged, officials said.
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)
By mid-evening, after a relative lull during the daylight hours, Israeli tank fire began intensifying and fatality reports poured in.
Five members of a single family were killed by tank fire on their home in northern Gaza's Beit Hanun, emergency services spokesman Ashraf al-Qudra said.
And four children were also killed by tank fire east of Gaza City, the youngest of them just two years old, he added.
The deaths, and those of others in the evening throughout Gaza, brought the number killed since midnight to 44, and raised the overall toll in 11 days of fighting in Gaza to 285 people killed.
An Israeli civilian and a soldier have also been killed.
Israel has said the aim of the ground operation is to destroy Hamas's network of tunnels which are used for cross-border attacks on southern Israel.
"It is not possible to deal with tunnels only from the air, so our soldiers are also doing that on the ground," Netanyahu said, although he admitted there was "no guarantee of 100% success."
The sky and the city is lit by Israeli forces' flares in the northern Gaza Strip. (AP photo)
Obama told reporters in Washington that the US supports Israel's right to defend itself, but also said Washington was "deeply concerned about the risks of further escalation and the loss of more innocent life."
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He added that Washington was "hopeful" that Israel would operate "in a way that minimises civilian casualties".
Israel pulled out all of its troops and settlers from Gaza in 2005, but within a year it became the de facto seat of Hamas after it won a landslide victory in Palestinian parliamentary elections.
Meanwhile, Abbas arrived in Turkey where he urged support for an Egyptian-brokered ceasefire proposal.
And French foreign minister Laurent Fabius said Abbas had urged Paris to ask Hamas allies Qatar and Turkey to pressure the group into accepting a ceasefire.
Shortly before Abbas arrived, Israel said it was pulling out some of its diplomatic staff following violent protests targeting its embassy and consulate buildings in Ankara and Istanbul.
Full coverage: Gaza under attack