Foreign Minister Gideon Saar told reporters in Jerusalem the war could end immediately if Hamas released the remaining hostages being held in Gaza and laid down its weapons.
"We will be more than happy to reach this objective with political means," he said.
In response, senior Hamas official Basem Naim told Reuters it would not lay down its arms but would release all of the hostages if Israel agreed to end the war and withdraw its forces from Gaza, a stance that has long been the Palestinian militant group's position.
Israel launched an assault in August on Gaza City, the major urban centre, and its forces are now just a few kilometres from the city centre.
Overnight, strikes killed 14 people across the city, local health officials said, including a strike on a school in southern Gaza City sheltering displaced Palestinians.
The military said it had struck a Hamas militant and that civilians had been warned before the strike was carried out.
Israeli forces would "continue to operate against the terrorist organisations in the Gaza Strip in order to remove any threat to Israeli civilians", a military spokesperson said.
The military pounded Gaza City at the weekend, destroying two high-rise buildings that were sheltering displaced Palestinians.
The military said the buildings were being used by Hamas and that civilians were warned in advance.
Israel has not provided any evidence to show Hamas was using the buildings, an accusation the militant group denied.
Israeli Prime Minister Benjamin Netanyahu has ordered the military to take Gaza City, where, according to a global hunger monitor, hundreds of thousands of Palestinians are facing famine.
Israeli officials acknowledge that hunger exists in Gaza, but deny the territory is facing famine.
Tens of thousands of Palestinians have been killed by Israel's military assault, launched after Hamas-led militants carried out the surprise October 7, 2023, attack that killed 1200 people and led to another 251 being abducted and taken into Gaza.
There are 48 hostages still held in Gaza. Israeli officials believe about 20 are still alive.
Most of the hostages who have been released were freed after indirect negotiations between Israel and Hamas.
Danish Foreign Minister Lars Lokke Rasmussen, speaking to reporters in Jerusalem alongside his Israeli counterpart, called on Israel to "change course" and stop its military campaign.
"We are extremely concerned about the humanitarian (situation)," he said, calling for the hostages to be freed.
Many Palestinians have fled Gaza City in recent weeks, but others have refused to leave, having already been displaced several times since the war started.
The military on Saturday warned civilians to leave for the south where hundreds of thousands of Palestinians are already sheltering in cramped tent encampments along the coast.
US President Donald Trump, who had promised a swift end to the war during his presidential campaign, on Friday said Washington was in "very deep" negotiations with Hamas.
Hamas official Naim said he hoped Trump was serious about reaching a deal, without directly acknowledging any negotiations.
Hamas has offered to release some hostages for a temporary ceasefire, similar to terms that were discussed in July before negotiations mediated by the US and Arab states collapsed.
On Saturday night, tens of thousands of protesters joined families of hostages at rallies, calling for an end to the war and demanding the release of the captives.
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