Israel's military said it sent in ground troops on Friday after days of fierce cross-border fire with Gaza, sparking fears the conflict was rapidly deteriorating into all-out war.
Israeli "air and ground forces are carrying out strikes on targets in the Gaza Strip", military spokesman Lt Col Jonathan Conricus said.
The military earlier said troops were operating in the Palestinian enclave, although Lt Col Conricus later said soldiers had not crossed the border.
The announcement came after Israel launched nearly 1,000 strikes on Palestinian territory since Monday, while Gaza militants fired about 1,750 rockets, the Israeli military said.
"I said that we would exact a very heavy price from Hamas and the other terrorist organisations," Israeli Prime Minister Benjamin Netanyahu said.
"We are doing so and we will continue to do so with great force."
At least 109 Gazans were killed and seven people in Israel, with children dead on both sides.
Some families fled their homes in Gaza on Thursday night and explosions erupted in the Palestinian enclave, while rockets were launched at Israel.
As the renewed assault got under way, Israel ordered residents living within four kilometres of the Gaza border to stay in shelters until further notice.
The initial news recalled Israel's ground offensive in Gaza in 2014, during a 50-day conflict in which 1,563 Palestinian and six Israeli civilians were killed.
International efforts to mediate an end to the conflict have so far failed, with the US objecting to a public meeting of the UN Security Council on Friday.
US Secretary of State Antony Blinken said Washington may support a meeting next week.
In addition to the casualties, the UN's humanitarian agency OCHA on Thursday reported "extensive damage" in Gaza to buildings, schools and infrastructure including electricity and water supplies.
Israel on Monday closed the goods and people crossings with Gaza and imposed a ban on fishing off the territory's coast, after rocket fire activated sirens in Jerusalem for the first time in seven years.
Hamas, which rules the Palestinian enclave, said it launched the attack in response to the actions of Israeli security forces in occupied East Jerusalem.
In the preceding days, hundreds of Palestinians and dozens of Israeli police officers were injured in violence at the Al Aqsa Mosque compound and elsewhere in East Jerusalem.
Israeli security forces have since faced a wave of intercommunal violence across the country, with Arab and Jewish mobs attacking people and setting cars ablaze.