Israel and Hamas for the first time in months are negotiating details of a possible deal to release Israeli hostages and for a temporary ceasefire in Gaza, according to two Israeli officials and a source with direct knowledge.

Why it matters: Both Israel and Hamas are under intense pressure to reach an agreement that would release the hostages and begin a humanitarian ceasefire in Gaza, where more than 30,000 Palestinians have been killed.

• Since December of last year, the talks mediated by Qatar and Egypt have been deadlocked in discussion about a framework for negotiations, rather than details of the actual agreement.
• The current proposal being negotiated could lead to a six-week ceasefire in Gaza and to the release of 40 hostages — women, female soldiers, men over the age of 50 and men in critical medical conditions — in return for hundreds of Palestinian prisoners.

Driving the news: The ongoing effort to reach a deal made progress last week when Hamas responded to a hostage deal framework proposed by the U.S., Qatar and Egypt.

• There are still gaps between the parties, but Hamas' response approached the original framework and allowed negotiations to progress to hammering out the details of a deal, Israeli officials said.
• The U.S. framework included the release of 400 Palestinian prisoners, including 15 who are serving life sentences for murdering Israelis, in return for 40 hostages.
• The Hamas response delivered last Thursday included the release of 950 prisoners, including 150 who are serving life sentences.

Friction point: Hamas wants choose which prisoners will be released, especially those who are serving life sentences. Israel has rejected that demand, per Israeli officials.

• On the other hand, Israel demands to receive in advance a list of the hostages who are alive and to deport the prisoners who are released to another country. Hamas has refused that, the officials said.
• But the two most widest gaps are Hamas' demand that the IDF withdraw from the corridor it created south of Gaza City, which prevents the return of Palestinians to the north of the Strip.
• The other sticking point is Hamas's demand that the next phase of the deal, which could include release of soldiers, includes a permanent ceasefire.

State of play: Israeli negotiators headed by Barnea met on Monday in Doha with Qatari and Egyptian mediators led by Qatari Prime Minister Mohammed Bin Abdulrahman al-Thani.

• A source with direct knowledge of the opening session of talks said it was positive. "Both parties came with some compromises and willingness to negotiate," the source said.
• A senior Israeli official said an Israeli negotiations team will stay in Doha to continue the detailed talks with Qatari and Egyptian mediators moving between the parties who are located in separate parts of the same compound in Doha.
• The official said the current round of talks could take at least two weeks. "It is going to be a long, difficult and complex process but we want to try and get a deal," he said.

Behind the scenes: The hostage deal is a political hot potato in Israel with Netanyahu's ultranationalist coalition partners objecting to any deal that will include a mass release of Palestinian prisoners and that could lead to a permanent ceasefire.

• Netanyahu last week postponed a cabinet meeting to discuss the mandate of the Israeli negotiations team for several days. On Sunday, he narrowed the mandate negotiators asked for in the hostage talks and laid stricter red lines for what they could accept in the negotiations, Israeli officials said.
• Some on the Israeli negotiations team are concerned Netanyahu's red lines will make a deal harder to achieve, but Mossad director David Barnea, who is heading the team, thinks it is still doable, an Israeli official said.
• "The negotiations team didn't get what it wanted but it got enough rope. If we will be close to a good deal, Netanyahu will give even more rope," a senior Israeli official said.