Qatar says it is hopeful that a Gaza ceasefire and hostage release deal could be agreed "very soon", with negotiators from Israel and Hamas beginning a "final stage" of indirect talks in Doha.
Foreign ministry spokesman Majed al-Ansari told reporters that major issues had been resolved in recent weeks and that drafts of a possible deal had been handed over to both sides.
However, he cautioned that "the most minor detail" could yet undermine the process, as has happened in the past during the 15-month war, reports BBC
Hamas's leaders expressed their satisfaction with the course of the negotiations. An Israeli official said there had been real progress, but stressed that "it's not there yet".
Under the proposed plan, during an initial six-week truce, Israeli hostages held by Hamas in Gaza would be exchanged at regular intervals for Palestinian prisoners jailed in Israel.
On Monday night, US President Joe Biden said a three-phase proposal based on what he had outlined last May was "on the brink" of finally coming to fruition.
There is new pressure for a deal, with Biden in his final week in office and President-elect Donald Trump warning that "all hell will break out" if the hostages are not released before his inauguration on Monday.
Israel launched a campaign to destroy Hamas in response to the group's October 7, 2023 attack, in which about 1,200 people were killed and 251 others were taken hostage.
More than 46,640 people have been killed in Gaza since then, according to the territory's Hamas-run health ministry.
Most of the 2.3 million population has also been displaced, there is widespread destruction, and there are severe shortages of food, fuel, medicine and shelter due to an struggle to get aid to those in need.
Israel says 94 of the hostages are still being held by Hamas, of whom 34 are presumed dead. In addition, there are four Israelis who were abducted before the war, two of whom are dead.
Qatar, Egypt and the US have for months been trying to broker a deal that would stop the fighting, secure the return of the remaining hostages, and allow a surge in humanitarian aid deliveries to Gaza.
Majed al-Ansari told a news conference in Doha on Tuesday that high-level talks on the final details were taking place there, describing them as "positive and productive".
He said mediators had delivered a draft proposal to the Israeli and Hamas negotiating teams and were hopeful that the talks "could lead very soon to an agreement".
"During the past months there were underlying issues, major issues, between the two parties that were unresolved. These issues were resolved during the past couple of weeks," he said.
However, he also urged people not to get "over-excited" until there was a formal announcement.
Although the underlying issues had been ironed out, he said, "this doesn't mean the deal is a reality". "We might be lost in the details, as was the case in the past," he added.
An Israeli government official told the BBC that "real progress" had been made in recent days, saying the talks had entered a critical and sensitive period.
"This is the only time since November 2023 that we are really negotiating with Hamas and they're not playing a game," he said, adding that the two sides were discussing "hundreds and thousands of details".
But, he said, while a deal was close, "it's not there yet".
Hamas - which Israel designates as a terrorist organisation, as does the US, UK and others - said in a statement that its leaders had informed other Palestinian factions of the "progress made in the negotiations".
The group also expressed hope that the current round would "end with a clear and comprehensive agreement".
There were signs that a deal was close on Monday, when a Palestinian official told the BBC that, for the first time in the war, delegations from Israel and Hamas had conducted six hours of indirect talks in the same building.
Revealing some potential details of the agreement, the official stated that "the detailed technical discussions took considerable time".
Both sides agreed that Hamas would release three hostages on the first day of the six-week initial truce, after which Israel would begin withdrawing the troops from populated areas, according to the official.
Seven days later, Hamas would release four additional hostages, and Israel would allow displaced people in the south of Gaza to return to the north, but only on foot via the coastal road.
Cars, animal-drawn carts, and trucks would be permitted to cross through a passage adjacent to main north-south Salah al-Din Road, monitored by an X-ray machine operated by a Qatari-Egyptian technical security team.
The agreement includes provisions for Israeli forces to remain in the Philadelphi corridor, a narrow strip of land running along Gaza's southern border with Egypt, and maintain an 800m-deep (2,600ft) buffer zone along Gaza's eastern and northern borders with Israel during the first phase.
The Palestinian official said Israel had also agreed to release 1,000 Palestinian prisoners, including approximately 190 who have been serving sentences of 15 years or more.
In exchange, he added, Hamas would release hostages, including women, the elderly and the sick or wounded.
The Israeli official said 33 names were on the list of hostages due to be released in the first phase, and that Israel was waiting for Hamas to confirm how many of them were still alive.
He said Israel was negotiating the "price" for nine ill and injured hostages due to be released in that phase, and that security arrangements for "hundreds" of Palestinian prisoners due to be released in exchange for the hostages were also now being discussed, with Israel stipulating that those convicted of murder would not be released into the occupied West Bank.
The Israeli official said the weakening of Hamas allies across the region, internal pressures on the group, and the involvement of both the outgoing and incoming US administrations had created "new possibilities" for a deal.
Israel, while it was focusing on the first stage of the proposed deal, was also keeping assets for future stages of negotiations, he added. "We will not leave the Gaza Strip until all our hostages are back home," he said.
Negotiations for the second and third phases of the agreement would begin on the 16th day of the ceasefire.
The second phase would see remaining hostages freed and troops withdrawn and the third would involve the reconstruction of Gaza.
Any deal would need to be approved by the Israeli cabinet, where Prime Minister Benjamin Netanyahu has faced opposition from far-right coalition partners.
On Tuesday, National Security Minister Itamar Ben-Gvir called the proposal "catastrophic", warning it would "effectively erase the hard-won achievements of the war".
The comments echoed those of Finance Minister Bezalel Smotrich, on whom Ben-Gvir called to join him in threatening to resign if the deal was agreed.
Sharon Lifshitz, a British-Israeli artist and filmmaker whose 84-year-old father Oded is one of the remaining hostages, told the BBC: "I'm trying to be optimistic. I'm trying to imagine it's possible that a deal will happen now and that all the hostages will return."
"For us, we know there will be so much heartbreak," she added. "We know quite a few of them are not alive anymore. We are desperate for the return first of the living ones so they can come back to their families."
She said her mother, Yocheved - who was also abducted in the October 7 attack but was released weeks later - was sceptical about the chances of a deal.
"She says that she would believe it when she sees them in our ambulances. But I think I can feel the cracks of optimism coming through a very long, dark period.
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