An airstrike also killed six journalists, including prominent Al Jazeera correspondent Anas Al Sharif, in a tent at a Gaza hospital compound.
Witnesses said Israeli tanks and planes pounded Sabra, Zeitoun, and Shejaia, three eastern suburbs of Gaza City in the north of the territory, on Monday, pushing many families out of their homes westwards.
Some Gaza City residents said it was one of the worst nights in weeks, raising fears of military preparations for a deeper offensive into their city.
According to Palestinian militant group Hamas, the area is now sheltering about one million people after the displacement of residents from the enclave's northern edges.
The Israeli military said its forces fired artillery at Hamas militants in the area.
There was no sign on the ground of forces moving deeper into Gaza City as part of the newly approved Israeli offensive, which is not expected to begin in the coming weeks.
"It sounded like the war was restarting," said Amr Salah, 25. "Tanks fired shells at houses, and several houses were hit, and the planes carried what we call fire rings, whereby several missiles landed on some roads in eastern Gaza," he told Reuters via a chat app.
The Israeli military said its forces on Sunday dismantled a launch site east of Gaza City, which Hamas used to fire rockets towards Israeli communities across the border.
Netanyahu on Sunday said he had instructed the Israeli military to speed up its plans for the new offensive.
"I want to end the war as quickly as possible, and that is why I have instructed the IDF (Israel Defence Forces) to shorten the schedule for seizing control of Gaza City," he said.
Netanyahu on Sunday said the new offensive will focus on Gaza City, which he described as Hamas' "capital of terrorism".
He also pointed to a map and indicated that the coastal area of central Gaza may be next, saying Hamas militants have been pushed there too.
The new plans have raised alarm abroad. On Friday, Germany, a key European ally, announced it would halt exports of military equipment to Israel that could be used in Gaza.
Britain and other European allies urged Israel to reconsider its decision to escalate the Gaza military campaign.
Mike Huckabee, the US ambassador to Israel, told Reuters some countries appeared to be putting pressure on Israel rather than on Hamas, whose deadly attack on Israel on October 7, 2023, ignited the war.
The airstrike that killed Al Jazeera's Anas Al Sharif and four of his colleagues at Al Shifa Hospital was the deadliest for journalists in the conflict so far and was condemned by journalists and rights groups.
Medics at the hospital said local freelancer Mohammad Al-Khaldi had also died in the attack, raising the number of dead journalists from the same strike to six.
Al Sharif had previously been threatened by Israel, which confirmed it had targeted and killed him, alleging he had headed a Hamas cell and was involved in rocket attacks against Israel.
Al Jazeera rejected the claim, and before his death, Al Sharif had also rejected Israeli allegations he had links to Hamas.
Hamas, which runs Gaza, linked his killing to the new planned offensive.
"The assassination of journalists and the intimidation of those who remain pave the way for a major crime that the occupation is planning to commit in Gaza City," it said.
