The violence between Israel forces and Palestinian militants entered a fifth day on Friday, with fresh air strikes, artillery fire, and rocket attacks.
The Israeli military said in a statement shortly after midnight that air and ground forces were attacking Gaza.
Rocket barrages from the Hamas-run enclave swiftly followed.
Witnesses said many families living in areas of Gaza near the border fled their homes, some seeking shelter at United Nations-run schools.
On Thursday, Israeli Prime Minister Benjamin Netanyahu said his country's military campaign "will take more time."
"The defence activity of Iron Dome batteries is giving us an offensive space and the IDF (Israeli Defence Forces) has already attacked hundreds of targets, we will soon pass 1,000 (targets). We continue striking Hamas while defending our citizens."
A funeral was held on Thursday for a Hamas commander killed in the Israeli strikes.
Since Monday, more than 100 people have been killed in Gaza, including dozens of children, medical officials said.
On the Israeli side, authorities said seven people had been killed, including a soldier who was laid to rest on Thursday.
International calls for an end to the hostilities have so far had no effect, as both sides show no sign of stepping down.
Tension has also spread to inside Israel with violent clashes reported in mixed communities of Jews and the Arab minority, prompting Israel's president to warn of a civil war.
The Israeli city of Lod was on edge Thursday night, as police patrolled the streets and made arrests.
The city has seen rioting, burning of cars, and violent attacks on individuals.
The UN Security Council will publicly discuss the worsening crisis on Sunday, diplomats said, after the U.S earlier objected to a meeting on Friday.
The 15-member council has met privately twice this week, but it has so far been unable to agree on a public statement.
Israel's escalating military conflict with Gaza is the worst since a 2014 war.