They set themselves a 48-hour deadline earlier this week, but today neither Hamas nor Israel had shown any signs of agreeing to a truce in Gaza despite pressure from international mediators.
The US, Egypt and Qatar put together a framework for a deal that would include a six-week halt to fighting and the exchange of about 40 hostages for hundreds of Palestinian prisoners.
It would also see increased humanitarian aid deliveries to Gaza and many displaced people returning to what is left of 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 withdrawal 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, said.
Israel accused Hamas of “walking away” from the offer.
“There is a very reasonable offer on the table and Hamas keeps walking away,” government spokesman David Mencer told reporters, adding that international pressure on Israel was “helping Hamas”.
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.
Mr Netanyahu has vowed to send ground troops into Rafah, ignoring an international outcry against it, including from the United States.
The war in Gaza broke out after Hamas militants attacked on Israel on 7 October, resulting in the deaths of 1,170 people, most of them civilians, according to an AFP tally of Israeli official figures.
Israel’s retaliatory offensive against Hamas has killed 33,482 people in Gaza, most of them women and children, according to the Hamas-run territory’s health ministry.
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Tactical truce
Analysts say Israel would benefit from a truce, even if it was just a tactical move, after losing 260 soldiers in Gaza.
On Sunday, Israel said it had withdrawn all its troops from southern Gaza, but had one brigade holding a central strip running across the territory.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 southern city of Khan Yunis, was all about preparing for an assault on Rafah.
As Israel is increasingly isolated over the high civilian death toll in Gaza, Mr 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 the United States is working to avoid an escalation in Lebanon, Syria and Iran, a 1 April 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 restraint by the army and an improvement in the humanitarian situation in Gaza.
Mr Netanyahu is also under immense pressure from desperate and angry families of the hostages still being held in Gaza.
Some 250 hostages were seized by Palestinian militants during the 7 October attack, of whom 129 are still being held. The military says 34 of them are dead.
Catching its breath
However, a truce could “shatter” Israel’s ruling coalition because of opposition from Mr Netanyahu’s far-right partners to any concessions to Hamas, said Mr Byman.
This is a real dilemma “for someone like Netanyahu who is not known for putting the country before his political ambition,” Mr Byman said.
Mr 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 leader of the group’s military wing.
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, Mr Abidi said.
He said that even if Mr Netanyahu promises a future without Hamas, the Islamist movement is already preparing “for the day after”.
