The US Secretary of State hopes that Hamas will accept what he described as the “very generous” Israeli offer for a truce in Gaza and a hostage release agreement.
Anthony Blinken was speaking while a Hamas delegation discussed the new proposal with mediators from Egypt and Qatar.
A source close to the talks told the BBC they were cautiously optimistic.
The proposal includes a 40-day truce in exchange for the release of the hostages and the possibility of allowing displaced families to return to northern Gaza.
The agreement also reportedly includes new language on restoring calm with the aim of meeting Hamas's demand for a permanent ceasefire.
Egypt's state-owned Cairo Channel said the Hamas delegation has now left Cairo and will return with a written response to the proposal.
The Israeli government is under increasing pressure from its global allies and the families of the hostages to reach an agreement.
Israel launched a military campaign to destroy Hamas in response to the group's cross-border attack on southern Israel on October 7, during which some 1,200 people were killed and 253 others were taken hostage.
More than 34,480 people have been killed in Gaza since then, according to the Hamas-run Health Ministry in the Strip.
The agreement reached in November saw Hamas release 105 hostages in exchange for a week-long ceasefire and about 240 Palestinian prisoners in Israeli prisons.
Mediators from Egypt, Qatar and the United States have been trying for weeks to broker a new agreement that would ensure another cessation of fighting and the release of 133 hostages that Israel says are still being held, at least 30 of whom are presumed dead.
Earlier this month, Hamas rejected an Israeli proposal for a six-week truce and the release of 40 women, children, the elderly and the sick in exchange for the release of hundreds of Palestinian prisoners.
Hamas said that it adheres to its demands for a permanent ceasefire that leads to a complete withdrawal of Israeli forces from Gaza and the return of displaced Palestinians to their homes.
The source close to the talks in Cairo told the BBC that the new proposal presented by Israel is very different from previous offers.
The officials said that the agreement also includes readiness “to discuss establishing a sustainable ceasefire within the framework of implementing the second phase of the agreement.”
Meanwhile, Israeli officials and a diplomat told the New York Times and Financial Times on Monday that Israel is also prepared to reduce the number of hostages released during the first phase to 33, down from 40.
Hamas has only publicly announced that it is studying the new Israeli proposal, but an unnamed senior official told Agence France-Presse on Sunday that “the atmosphere is positive unless there are new Israeli obstacles.”
He added: “There are no major issues in the observations and inquiries submitted by Hamas regarding their content [of the proposal],” they added.
Blinken also expressed his optimism during the World Economic Forum meeting in Riyadh, which was attended by a number of his European and Arab counterparts.
He said, “Hamas has an unusual and very generous proposal from Israel. At this moment, the only thing standing between the people of Gaza and a ceasefire is Hamas.”
“They have to decide, and they have to decide quickly…and I hope they make the right decision.”
Egyptian Foreign Minister Sameh Shoukry, whose country plays a mediating role in negotiations between Israel and Hamas alongside Qatar, said he was “optimistic.”
He added, “The proposal took into account the positions of both sides and tried to extract moderation.” He added: “There are factors that will have an impact on the decisions of both sides, but I hope that everyone will rise to the occasion.”
Sunday's phone call between US President Joe Biden and Israeli Prime Minister Benjamin Netanyahu is said to have focused on negotiations.
They also discussed the need to maintain the recent increase in aid reaching Gaza and continued US opposition to a large-scale attack on the southern city of Rafah, where more than a million displaced people are sheltering.
Local medics and rescue workers said that at least 22 Palestinians were killed in Israeli air strikes on three homes in Rafah overnight.
“We call on the whole world for a permanent truce. That is enough,” a man named Abu Taha told AFP at Al-Najjar Hospital, as a crowd of his relatives mourned the shrouded bodies.
There was no immediate comment on the reports from the Israeli army.
Meanwhile, children in Rafah told BBC Arabic's Gaza Today radio program that rising temperatures were making life unbearable in the thousands of tents and temporary shelters set up there.
Sarah Abu Amr, 11 years old, said: “Being inside the tent does not protect me from the intense heat, as if I were standing directly under the sun’s rays.”
“There is no electricity to run fans or get cold water to mitigate the terrible effect of the heat, and there is no food, water or anything at all to keep us hydrated.”
Last week, when temperatures reached 40 degrees Celsius (104 Fahrenheit), a five-month-old baby girl reportedly died in a tent due to the extreme heat. According to the United Nations.
Over the weekend, there were further indications from senior Israeli generals that plans had been finalized for a major operation in Rafah, where the military says Hamas brigades and their remaining leaders are based.
But Blinken – who is scheduled to travel from Saudi Arabia to Jordan and Israel – noted that the United States “has not yet seen a plan that gives us confidence that civilians can be effectively protected.”
Palestinian Authority President Mahmoud Abbas – a rival to Hamas based in the occupied West Bank – said on Sunday that the United States was the only country capable of preventing the attack on Rafah, which he warned could cause “the biggest catastrophe in Israel's history.” Palestinian people”.
Israeli Foreign Minister Israel Katz said on Sunday that the Israeli army would “suspend the operation” in Rafah if a hostage release deal was agreed upon.
But far-right Finance Minister Bezalel Smotrich warned Netanyahu against canceling the Rafah attack, saying that if he failed to destroy Hamas, “the government he heads will have no right to exist.”
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