Middle East live updates: Israel, Hamas closer to ceasefire than ever before

Israel and the highest ranks of Hamas have now agreed to the core elements of the hostage release-ceasefire deal on the table, but both sides are continuing to haggle over the details of the proposal, according to two officials familiar with the negotiations.

The outstanding differences are seen as relatively minor, but talks are expected to continue into Wednesday, the officials said.

Many of the items that are still being ironed out are tied to stubborn sticking points that have emerged in the past, like the operation of the Rafah border crossing and Israeli security concerns connected to the movement of displaced Palestinians back to their homes in northern Gaza.

The disagreements are unlikely to derail progress at this point, according to the officials.

Two of the three Americans that are possibly alive inside Gaza are poised to be released in the initial days or weeks of the ceasefire if an agreement is reached, but an official said they expect the releases will happen slower than they did during the truce in November 2023.

While they don’t have recent proof of life for the two Americans, the assumption is that they and most -- but not all -- of the 33 hostages freed under the deal will be returned alive.

-ABC News' Shannon K. Kingston

Israel is currently waiting to hear back from Hamas on the most recent draft language of a ceasefire deal, sources told ABC News.

The two sides are reportedly closer to an agreement than ever before, according to a spokesperson for Qatar Foreign Minister Sheikh Mohammed bin Abdulrahman bin Jassim bin Jabr Al Thani.

"The ongoing talks in Doha regarding Gaza are fruitful, positive and focus on the final details. Meetings are underway in Doha between the parties to the agreement and we are awaiting updates from them," the spokesperson told ABC News.

Implementation of the agreement will begin shortly after it is announced, according to the spokesperson.

Qatar's Foreign Ministry spokesperson said at a Tuesday briefing that participants in the ongoing Gaza ceasefire talks in Doha are close to a ceasefire deal.

"We expect the agreement to be announced soon," the spokesperson said during the press conference.

Qatar is a key mediator between Israel and Hamas and has hosted several rounds of ceasefire talks in the capital Doha.

-ABC News' Nasser Atta

The Gaza Ministry of Health said Tuesday that Israel Defense Forces strikes killed at least 61 Palestinians in the previous 24 hours and injured 281 more in the Hamas-run territory.

The total number of Palestinians killed since the war broke out on Oct. 7, 2023, is now 46,645 with 110,012 people injured, according to the ministry.

-ABC News' Somayeh Malekian