Prime Minister Benjamin Netanyahu is set to convene Israel's war cabinet and then his full government Tuesday amid progress in negotiations for a temporary cease-fire in the country's war with the Palestinian group Hamas that's expected to see some Israeli hostages released. 

The proposed deal will allow for an initial group of 50 hostages held by Hamas to be released in phases during windows of pause, CBS News has confirmed. The proposed deal, brokered by the U.S. and Qatar, will include a limited six-hour pause in fighting for four days, according to sources familiar with the agreement. 

During this time, aid will also be allowed into Gaza, with a total of 300 trucks carrying aid, including cooking oil for bakeries and fuel for hospitals, a source familiar told CBS News.

The deal will allow for the release of Palestinian prisoners — women and children — held in Israel detention centers, with three Palestinian prisoners released for each hostage held by Hamas, CBS News has confirmed. 

If the first phase goes as planned, roughly 20 more hostages will be released by Hamas and the pause in fighting extended. 

Children, estimated to be around 40 in number among the hostages in Gaza, were set to be given priority in the initial batch of captives released by Hamas. Among the hostages taken by Hamas, there is one American child, a 3-year-old girl. 

Sources informed CBS News that the deal is expected to result in the liberation of at least 75 hostages, and possibly more, in stages by Hamas.

"We are making progress. I don't want to say too much, not even at this moment, but I hope there will be positive news soon," Netanyahu told reservists on Tuesday, without providing further details.

The terms of the agreement have not yet been officially confirmed by Israel. 

"In light of the developments regarding the release of our abductees — the Prime Minister will convene the War Cabinet at 18:00, the Political-Security Cabinet at 19:00 and the Government at 20:00," Netanyahu's office stated in a social media post on Tuesday. The timing of the last meeting, which involves the entire Israeli government, is 8 p.m. local time, equivalent to 1 p.m. Eastern. 

Israel's Supreme Court would also need to approve any deal involving the release of Palestinian prisoners, but the court can choose to waive its approval and refer the decision back to the government.

• Hope, but no relief yet for Gaza's displaced, or for Israeli hostages' families

Officials with knowledge of the negotiations, including President Biden, have been saying for days that an agreement appears to be getting closer. 

Hostage Release Agreement and Cease-fire

"We've been working on this intensively for weeks, as you all know," a spokesperson said Tuesday at the White House. "We're now very close, very close. We could bring some of these hostages home very soon. But I don't want to get into the details of things because nothing is done until it's done. And when we have more to say, we will, but things are looking good at the moment."

The details of the long-sought hostage release agreement and short-term cease-fire were still coming to light Tuesday ahead of the Israeli government meetings.

A senior member of the opposing group told CBS News that the agreement was for the group to hand over 50 hostages in exchange for the release of 150 prisoners, or three prisoners freed for every abducted person released. But there is no set cap on the number of prisoners to be released.

A source familiar with the talks told CBS News that those numbers were not limits, and that the potential cease-fire — expected to be around five days initially — could be extended if the opposing group continues releasing hostages. More prisoners could also be released, with officials suggesting a ratio of three prisoners to walk in exchange for every hostage that comes home.

The source said most of the prisoners would be released to live in a specific region, though some did come from another area.