Boys play with a toy car, as displaced Palestinians, who fled their houses due to Israeli strikes, take shelter in a tent camp at the border with Egypt in Rafah on Wednesday. Reuters

Israeli Prime Minister Benjamin Netanyahu said on Wednesday total victory in Gaza was within reach, rejecting the latest offer from Hamas for a ceasefire to ensure the return of hostages still held in the besieged enclave.

Netanyahu renewed a pledge to destroy the Palestinian movement, saying there was no alternative for Israel but bringing about the collapse of Hamas.

"The day after is the day after Hamas. All of Hamas," he told a press conference, insisting that total victory against Hamas was the only solution to the Gaza war.

Hamas had proposed a Gaza ceasefire of four-and-a-half months, during which all hostages would go free, Israel would withdraw its troops from the Gaza Strip and an agreement would be reached on an end to the war.

Earlier Hamas has proposed a ceasefire to quiet the guns in Gaza for four-and-a-half months, during which all hostages would go free, Israel would withdraw its troops from the Gaza Strip and an agreement would be reached on an end to the war.

The group's proposal - a response to an offer sent last week by Qatari and Egyptian mediators and cleared by Israel and the United States - came during the biggest diplomatic push yet for an extended halt to the fighting.

Israel's Channel 13 cited a senior official as saying some of the demands presented by Hamas were not acceptable to Israel, without providing details. Israel has previously said it will not pull its troops out of Gaza until Hamas is wiped out.

The report quoted the unidentified official as saying Israeli authorities would debate whether to reject Hamas's proposals outright or ask for alternative conditions.

But the Hamas offer, in a document seen by Reuters and confirmed by sources, appears to finesse Hamas's longstanding demand for a full end to the war as a pre-condition before releasing hostages it seized on Oct. 7 in the raid that precipitated Israel's assault.

US Secretary of State Antony Blinken, who arrived overnight in Israel after meeting the leaders of mediators Qatar and Egypt, met Israeli Prime Minister Benjamin Netanyahu to discuss the proposal.

A source close to the negotiations said the Hamas counterproposal did not require a guarantee of a permanent ceasefire at the outset, but that an end to the war would have to be agreed during the truce before final hostages were freed.

A second source said Hamas still wanted guarantees from Qatar, Egypt and other friendly states that the ceasefire would be upheld and not collapse as soon as hostages go free.

"They want the aggression to stop and not temporarily, not where (the Israelis) take the hostages and then the Palestinian people live in a grinder."

Ezzat El Reshiq, a member of the Hamas political bureau, confirmed the offer had been passed via Egypt and Qatar to Israel and the United States.

"We were keen to deal with it in a positive spirit to stop the aggression against our Palestinian people and secure a complete and lasting ceasefire as well as provide relief, aid, shelter and reconstruction," he said.

According to the document, during the first 45-day phase, all Israeli women hostages, males under 19 and the elderly and sick would be released, in exchange for Palestinian women and children held in Israeli jails. Israel would withdraw troops from populated areas.

Implementation of the second phase would not begin until the sides conclude "indirect talks over the requirements needed to end the mutual military operations and return to complete calm".

The second phase would include the release of remaining male hostages and full Israeli withdrawal from all of Gaza. Bodies and remains would be exchanged during the third phase.

"People are optimistic, at the same time they pray that this hope turns into a real agreement that will end the war," Yamen Hamad, a father of four sheltering in a UN school in Deir Al-Balah in the central Gaza Strip told Reuters via a messaging app.

In Rafah, on the southern edge of the Gaza Strip where half of the enclave's 2.3 million people are penned against the border fence with Egypt, the bodies of 10 people killed by Israeli strikes overnight were laid out in a hospital morgue.

At least two of the shrouded bundles were the size of small children. Relatives wept beside the dead.

Israel began its military offensive after militants from Hamas-ruled Gaza killed 1,200 people and took 253 hostages in southern Israel on Oct. 7. Gaza's Health Ministry says at least 27,585 Palestinians have been confirmed killed, with thousands more feared buried under rubble.

There has been only one truce so far, lasting just a week at the end of November.

Netanyahu is under competing pressure from far-right members of his coalition government who say they will quit rather than endorse any deal that fails to eradicate Hamas, and from families of hostages who demand a deal to bring them home.

Washington has cast the hostage and truce deal as part of plans for a wider resolution of the Middle East conflict, ultimately leading to reconciliation between Israel and Arab neighbours and the creation of a Palestinian state.

"We will be working as hard as we possibly can to try to get an agreement so that we can move forward with - not only a renewed but an expanded agreement on hostages - and all the benefits that that would bring with it,” Blinken said at a news conference in Doha late on Tuesday.

Last week, Israel said it plans to storm Rafah, raising alarm among international aid organisations who say an assault on the last refuge at Gaza's edge would cause a humanitarian catastrophe for more than a million displaced people.