Hamas-run Gaza's health ministry reported at least 165 people killed over the previous 24 hours -- more than double Friday's toll.
An AFP correspondent reported gunfire, air strikes and tank shelling that was especially heavy in Khan Yunis, souther Gaza's main city.
Witnesses also told AFP that Israeli boats were bombarding Gaza City and other areas in the north early on Sunday.
In Rafah, near the border with Egypt, at least five people were killed in a strike that hit what the Gaza health ministry said was a civilian car.
Israel is pressing its push southwards against Hamas, after the military said in early January the militants' command structure in northern Gaza had been dismantled, leaving only isolated fighters.
But Hamas has also reported heavy combat in the north of Gaza as Israel's military said its troops, backed by air and naval support, were striking militant infrastructure throughout the Palestinian territory.
Israel has vowed to destroy Hamas in response to the group's unprecedented October attacks that resulted in the deaths of about 1,140 people, mostly civilians, according to an AFP tally based on official Israeli figures.
Israel's relentless bombardment and ground offensive have killed at least 24,927 people in Gaza, mostly women and children, according to the Gaza health ministry.
Violence has also surged in the Israeli-occupied West Bank, where the military said it had demolished two houses in Hebron that it said had belonged to two Palestinian gunmen who had carried out an attack on a road between Jerusalem and Bethlehem in November.
The official Palestinian news agency Wafa reported clashes between Israeli troops and Palestinian fighters in the West Bank village of Maithalun, south of Jenin, as well as in the West Bank towns of Arura and Qalqilya.
'Retain control'
The United States, which provides Israel with billions of dollars in military aid, has urged it to take more care to protect civilians but they have disagreed over Gaza's future governance.
Netanyahu and US President Joe Biden discussed the post-war future of Gaza in a call on Friday, their first in almost a month.
Biden said it was still possible Netanyahu could agree to some form of Palestinian state, but Netanyahu's office said in a statement on Saturday Israel "must retain security control over Gaza to ensure that Gaza will no longer pose a threat to Israel."
That, it said, was "a requirement that contradicts the demand for Palestinian sovereignty."
UN Secretary-General Antonio Guterres said at the Non-Aligned Movement summit in Uganda the Palestinian right to statehood "must be recognised by all" and that its denial was "unacceptable."
The UN agency for Palestinian refugees UNRWA says about 1.7 million people have been displaced in Gaza, with about one million crowded into the Rafah area.
The UN humanitarian agency OCHA reported just 15 bakeries operating across Gaza and that the availability of water "is shrinking every day."
UN agencies have warned better aid access is needed urgently as famine and disease loom.
Spy chief
The war has sent regional tensions soaring, with a surge in violence involving Iran-backed Hamas allies from Lebanon to Yemen and beyond.
Iranian media said an Israeli strike on Damascus killed the Revolutionary Guards' spy chief in Syria and four other Guards members, prompting a threat of retaliation from Tehran's foreign ministry.
Israel, which declined to comment on the Damascus strike, has intensified attacks on targets in Syria since the October 7 attacks.
Deadly exchanges have also occurred regularly between Israeli forces and Lebanon's Iran-backed Hezbollah.
Lebanon's official National News Agency reported two deaths in an Israeli strike on Saturday, and Hezbollah later said one of its fighters had been killed.
In western Iraq, a military base used by US-led coalition forces came under missile attack, US Central Command said.
The Tehran-aligned Islamic Resistance in Iraq claimed responsibility for the attack.
The US military also said it carried out fresh strikes on Saturday against Yemen's Huthi rebels, who say they have been hitting Israeli-linked shipping in the vital Red Sea shipping lanes in solidarity with Gaza.
'Elections now'
Militants also seized about 250 hostages during the October attacks.
Israel says around 132 remain in Gaza, of whom at least 27 captives are believed to have been killed, according to an AFP tally based on Israeli figures.
Israelis rallied in Tel Aviv, Haifa and near Netanyahu's Jerusalem residence on Saturday, demanding action to secure their release.
Some carried banners calling for "elections now" to replace Netanyahu's hard-right government over its handling of the war.
"The way we're going, all the hostages are going to die. It's not too late to free them," Avi Lulu Shamriz, the father of Alon Shamriz, a hostage mistakenly killed by Israeli troops last month, told AFP in Tel Aviv.
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