They set themselves a 48-hour deadline earlier this week, but on Thursday neither Hamas nor Israel had shown any signs of agreeing to a truce in Gaza despite pressure from international mediators.
The United States, Egypt and Qatar put together a framework for a deal that would include a halt in fighting for six weeks and the exchange of about 40 hostages for hundreds of Palestinian prisoners.
It would also see increasing humanitarian aid to Gaza and many displaced people returning to their homes.
The proposals ultimately aim to secure the release of all 129 hostages believed to still be alive in Gaza, along with the eventual exit of all Israeli troops.
But now “negotiations are at an impasse”, said Hasni Abidi of the Geneva-based Centre for Studies and Research for the Arab and Mediterranean World.
However, no side has yet given up.
“Hamas is studying the offer... It has not responded yet,” a Hamas spokesman in Doha, Hossam Badran, told AFP.
Hamas wants a permanent ceasefire in Gaza, which at this stage is unacceptable to Israeli Prime Minister Benjamin Netanyahu, who has vowed to "eliminate" all Hamas battalions.
He said four battalions continue to operate in Rafah, the last stronghold of Hamas in southern Gaza, where some 1.5 million Palestinians have taken refuge.
Netanyahu has vowed to launch a ground invasion of Rafah, ignoring an international outcry against it, including from the United States, Israel's strongest ally.
The war in Gaza broke out after Hamas militants carried out an unprecedented attack on Israel on October 7, targeting several Israeli communities in southern Israel.
That attack resulted in the deaths of 1,170 people, most of them civilians, according to an AFP tally based on official Israeli figures.
In retaliation Israel vowed to destroy Hamas, and its blistering military campaign since then has already killed 33,482 people, most of them women and children, according to the health ministry in Hamas-run Gaza.
Tactical truce
Analysts feel that Israel would benefit from a truce, even if it was just a tactical move, given that it has lost 260 soldiers inside Gaza already with thousands more injured.
On Sunday, Israel said it had withdrawn all its troops from southern Gaza, but had one brigade holding a central strip running across the territory.
Daniel Byman of the Georgetown University School of Foreign Service said pulling out those soldiers, including from the city of Khan Yunis, was all about preparing for an assault on Rafah.
As Israel is increasingly isolated diplomatically over the high civilian casualties in Gaza, Abidi said, the drawdown gives it much needed breathing space, especially when it comes to handling Washington, which it "has failed to convince" when it comes to its war strategy.
While Washington is working to avoid an escalation in Lebanon, Syria and Iran, an April 1 strike on the Iranian consulate in Damascus that was widely blamed on Israel risks "shattering" this strategy, he said.
An exasperated US President Joe Biden has vowed to continue supporting Israel, but this is dependent on its military restraint and improvement in humanitarian assistance to Gazans.
Netanyahu is also under immense pressure from desperate and angry families of the hostages still being held in Gaza.
Some 250 Israelis and foreigners were seized during the October 7 attack by Palestinian militants, of whom 129 are still being held. The military says 34 of them are dead.
Catching its breath
However, a truce could “shatter” the ruling Israeli coalition because of opposition from its far-right members to any concessions to Hamas, said Byman.
This is a real dilemma “for someone like Netanyahu who is not known for putting the country before his political ambition,” he said.
Abidi said “I don't see how Netanyahu could claim victory if none of the top” Hamas operatives in Gaza are captured or killed.
Israeli officials are particularly targeting Yahya Sinwar, the head of Hamas in Gaza, and Mohammed Deif, the military leader of the group there.
Sinwar has been accused of being the mastermind of the October 7 attack.
But for Hamas a truce would be a symbolic victory.
It would also allow it "to reorganise and carry out ambushes against the (Israeli) army", said Omer Dostri of the Jerusalem Institute for Strategy and Security.
“Hamas's goal is to catch its breath in the hope that international pressure will eventually bring about an end to the war,” he said.
A truce would also make Hamas look better in the eyes of the battered and hungry population of Gaza, said Abidi.
He said that even if Netanyahu promises a future without Hamas in the small coastal territory, the Islamist movement is already preparing "for the day after".
AFP