Large explosions shook Gaza City early on Thursday, just hours after Israel pledged to keep pummelling the Palestinian militant group Hamas.
Earlier, Hamas fired a barrage of rockets into Israel, targeting Jerusalem and Tel Aviv.
One rocket hit an apartment building in the city of Petah Tikva.
There were no immediate reports of casualties.
Israel on Thursday began preparing ground troops along the Gaza border.
This week has seen the most intense conflict between the two sides since 2014, and has prompted Washington to send a top diplomat to the Middle East.
At least 67 people have been killed in Gaza since Monday, according to the enclave's health ministry.
Seven people have been killed in Israel, medical officials said.
In a phone call with U.S. President Joe Biden, Prime Minister Benjamin Netanyahu said Israel would continue to target the military capabilities of Hamas.
Still - Biden said he was confident the hostilities would end soon.
"My expectation and hope is this will be closing down sooner than later, but Israel has a right to defend itself."
But like Netanyahu, Palestinian President Mahmoud Abbas remains defiant:
"I direct my speech specifically to America and Israel, we are fed up, go away from us, leave us. We will stay like a thorn in your eyes, we will never leave our country, end your occupation today, before tomorrow.
There have been clashes between Palestinians and Israeli forces in the West Bank.
Violence also flared in mixed Jewish-Arab towns in Israel, like Lod.
Explosions could be heard and police vehicles were set on fire, despite the police imposing a rare night-time curfew.
In the Israeli town of Bat Yam, a crowd of Jewish rioters attacked an Arab driver on Wednesday night, according to Israeli media.
Video showed the driver being dragged out of his car by men who attacked him until he was left bleeding on the ground.
Israel's president has warned of a civil war between the country's Arabs and Jews.
The violence follows weeks of tension, and clashes between Israeli police and Palestinian protesters outside the Al-Aqsa Mosque in Jerusalem during the holy Muslim month of Ramadan.
These escalated in recent days ahead of a now postponed court hearing about Palestinian families being evicted from East Jerusalem homes claimed by Jewish settlers.