Israel bombarded the Gaza Strip and battled Hamas Sunday as mediators called on both sides to agree to a truce and hostage release deal outlined by US President Joe Biden.

Since Biden spoke at the White House on Friday, Prime Minister Benjamin Netanyahu has insisted Israel will pursue the war, now nearing its ninth month, until it has destroyed Hamas and freed the captives.

Netanyahu, a hawkish political veteran leading a fragile right-wing coalition government, is under intense domestic pressure from two sides.

Protesters backing an immediate hostage release, who rallied again Saturday in Tel Aviv, want him to strike a truce deal, but his 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.

Fighting rocked Gaza overnight and Sunday, with Israel's military reporting 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 Hamas.

Netanyahu said 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".

White House National Security Council spokesman John Kirby told ABC News Sunday that "we have every expectation that if Hamas agrees to the proposal, as was transmitted to them -- an Israeli proposal -- that Israel would say yes."

"We're waiting for an official response from Hamas," he added.

Bd pratidin English/Lutful Hoque