Palestinian militant group Hamas, meanwhile, has said it "views positively" what Biden described as an Israeli proposal.
Netanyahu, a hawkish political veteran leading a fragile right-wing coalition government, is under intense domestic pressure from two sides.
Protesters backing immediate hostage release, who rallied again Saturday in their tens of thousands in Tel Aviv, are urging him to strike a truce deal, while the premier's far-right allies are threatening to bring down the government if he does.
Opposition leader Yair Lapid has offered Netanyahu political support if the government secures a deal.
Palestinian children walk past destroyed buildings in the Jabalia refugee camp in northern Gaza. (Omar Al-Qattaa / AFP)
Deadly fighting rocked Gaza overnight and Sunday, with the Israeli military reporting more air strikes and ground combat.
Across Gaza, the military said Sunday it had struck "30 terror targets" over the past day including "weapons storage facilities" and militants.
Netanyahu said on Saturday that "Israel's conditions for ending the war have not changed: the destruction of Hamas's military and governing capabilities, the freeing of all hostages and ensuring that Gaza no longer poses a threat to Israel".
Mediators the United States, Qatar and Egypt later said they "call on both Hamas and Israel to finalise the agreement embodying the principles outlined by President Joe Biden".
Political pressure
According to Biden, Israel's three-stage offer would begin with a six-week phase that would see Israeli forces withdraw from all populated areas of the Gaza Strip and an initial hostage-prisoner exchange.
Israel and the Palestinians would then negotiate for a lasting ceasefire, with the truce to continue so long as talks are ongoing, Biden said, adding it was "time for this war to end".
Netanyahu took issue with Biden's presentation, insisting that according to the "exact outline proposed by Israel" the transition from one stage to the next was "conditional" and crafted to allow it to maintain its war aims.
Finance Minister Bezalel Smotrich and National Security Minister Itamar Ben Gvir, leaders of the two extreme-right parties in parliament, warned they would leave the government if it endorsed the truce proposal -- potentially costing Netanyahu's coalition its majority.
Map of the Gaza Strip. (Sylvie Husson, Sabrina Blanchard / AFP)
Smotrich said he also opposed the return of displaced Gazans to the territory's north and the "wholesale release of terrorists" in a prisoner swap.
Lapid, a centrist former premier, said that the government "cannot ignore Biden's important speech" and vowed to back Netanyahu if his far-right coalition partners quit.
"I remind Netanyahu that he has our safety net for a hostage deal," Lapid said on X.
Helicopter strikes
The Gaza war was sparked by Hamas's unprecedented October 7 attack, which resulted in the deaths of 1,189 people, mostly civilians, according to an AFP tally based on Israeli official figures.
Militants also took 252 hostages, 121 of whom remain in Gaza, including 37 the army says are dead.
Israel's retaliatory bombardments and ground offensive have killed at least 36,439 people in Gaza, mostly civilians, according to the Hamas-run territory's health ministry.
Heavy fighting has flared in far-southern Rafah, where Israel sent tanks and troops in early May, ignoring concerns for displaced civilians sheltering in the city.
The UN agency for Palestinian refugees, UNRWA, said on Sunday that all 36 of its shelters in Rafah "are now empty", after at least a million civilians have fled the city that until last month was sheltering 1.4 million people.
"The humanitarian space continues to shrink," UNRWA said, adding that about 1.7 million people were now sheltering in southern Gaza's main city of Khan Yunis and in central areas of the territory.
Witnesses said Israeli Apache attack helicopters on Sunday opened fire on targets in central Rafah, a jet fired a missile at a house in the western Tal al-Sultan district and artillery shelling targeted the southern Brazil neighborhood.
There were also ongoing clashes in Rafah including fighting in the city centre and drone attacks, witnesses told AFP.
Cairo meeting on Rafah crossing
The Palestinian Red Crescent said it was "very difficult" to access the city, on the border with Egypt, because of the Israeli bombardment, adding that two of its staff had been killed on Friday by Israeli fire.
In the besieged territory's north, Israeli helicopters fired at Gaza City's Zeitun and Sabra areas, and an air strike hit a house in the city's east, AFP reporters said.
A hospital medic said three people were killed when an air strike hit a family apartment in Gaza City's Daraj neighbourhood.
The Israeli seizure of the Rafah crossing last month has further slowed sporadic aid deliveries for Gaza's 2.4 million people and effectively shuttered the territory's main exit point.
Egyptian state-linked Al-Qahera News said Cairo was due to host a meeting Sunday with Israeli and US officials to discuss reopening the Rafah crossing.
Egypt, which refuses to coordinate with Israel passage through Rafah, has agreed to send some aid via Israel's Kerem Shalom crossing.
Israel's defence ministry body overseeing civilian affairs in the Palestinian territories, COGAT, said 764 Egyptian trucks had crossed into Gaza over the past week through Kerem Shalom.
