GEOFF BENNETT: Turning our focus now to the Middle East, where mediators working toward a Gaza cease-fire wrapped up a second day of talks and, by some indications, ended on a hopeful note.

Nick Schifrin joins us with more.

Nick, it's good to see you.

So where do these talks stand right now?

NICK SCHIFRIN: As you said, Geoff, U.S. officials are hopeful, even optimistic.

A senior administration official who briefed reporters this afternoon used phrases like this -- quote - - "This process is now in the endgame, a deal that is ready to be closed.

The package is basically there."

But, crucially, there is still no Israeli and Hamas agreement to new language that U.S., Qatari and Egyptian mediators today called a bridging proposal.

Now, recall that there is an overall agreement on the framework of the first phase of this deal, six-week cease-fire, the release of more than 30 hostages from Hamas and 700 Palestinian detainees released by Israel, and a humanitarian aid surge alongside a phased Israeli withdrawal from Gaza.

But there are disagreements and the new language is designed to bridge these disputes.

So, number one, the senior officials said, on Israel's insistence to control the Philadelphi Corridor between Gaza and Egypt -- quote -- "That issue is moving the right way."

Number two, on checkpoints inside Gaza that Israel insists on, the official said the agreement aimed to block Gazans who might move from the south to the north with weapons.

And, number three, in the coming days, working groups will examine which Israeli hostages and Palestinian prisoners will be released and in what sequence.

The U.S., Egypt and Qatar said today that they will aim to -- quote -- "conclude the deal next week in Cairo when they reconvene."

President Biden said, "We're closer than we have ever been."

But, again, there's no confirmation from Israel or Hamas, the two sides fighting this war, that they will agree to language that the U.S. hopes not only pauses the war, but also blocks an Iranian attack on Israel.

GEOFF BENNETT: Well, what do officials say about the possibility of such an attack?

NICK SCHIFRIN: They are still very worried about that because they have seen Iran make preparations for that attack.

President Biden explicitly said tonight no one in the region, i.e., Iran, should launch an attack that could derail the negotiations.

So if holding out hope for a Gaza cease-fire, if you will, is the kind of carrot to Iran, the administration also delivered a stick, a explicit warning to Iran.

The senior administration official said of Iran's warning that it might strike Israel, he said -- quote -- "We would also encourage the Iranians, and I know many are, not to move down that road because the consequences could be quite cataclysmic, particularly for Iran."

That is not language that this administration often uses.

Tomorrow night, Secretary of State Tony Blinken, you see him there on a previous trip to Israel, will travel to Israel again to meet Israeli Prime Minister Benjamin Netanyahu, a visit designed to underscore that U.S. message on Iran, but also, crucially, Geoff, try to make sure the Netanyahu agrees to the cease-fire language that is coming out today.

Because, again, that other administration official warned Israel today -- quote -- "If you continue to negotiate for months and months and try and get the perfect deal, you risk having no hostages left to save."

GEOFF BENNETT: All right, Nick Schifrin, thanks, as always.

NICK SCHIFRIN: Thank you.

GEOFF BENNETT: Appreciate it.