WILLIAM BRANGHAM: Today, at the Pentagon, Secretary of Defense Lloyd Austin presented an alternative vision to Israel stated assault plan on the Southern Gazan city of Rafah.

More than one million Gazans have fled their homes and are now sheltering there.

Austin and Israeli Defense Minister Yoav Gallant met today as negotiations over a cease-fire and hostage release seemed to hit an impasse.

Nick Schifrin is following it all, and he joins me now.

Nick, so how did this meeting today between Austin and Gallant go?

NICK SCHIFRIN: As you said, William, Austin laid out an alternative vision that the U.S. sees that Israel should use in order to go into Rafah to Gallant, who's here on a prescheduled visit separate from that delegation we spoke about last night that Benjamin Netanyahu, the prime minister of Israel, had canceled.

The U.S. agrees with Israel that Israel needs to go after Hamas' final four battalions that are hiding among the population in Rafah.

It just disagrees with how to go about doing that.

And according to a senior defense official, Austin laid out a U.S. vision that includes precision targeting of senior Hamas leaders, securing the border with Egypt, and ensuring that humanitarian assistance goes into Rafah and civilians leave Rafah in the right sequence.

The senior defense official who spoke to us earlier pointed out that Rafah is not only home to 1.5 million displaced Gazans, many of whom have been displaced twice.

It's also strategically important for aid.

Rafah City is right next to Rafah, the border crossing, and the Kerem Shalom crossing, through which aid needs to arrive into Gaza.

And U.S. officials are imploring Israel to allow more aid into Gaza, as Secretary of Defense Lloyd Austin said today.

LLOYD AUSTIN, U.S. Secretary of Defense: Protecting Palestinian civilians from harm is both a moral necessity and a strategic imperative.

In Gaza today, the number of civilian casualties is far too high, and the amount of humanitarian aid is far too low.

Gaza is suffering a humanitarian catastrophe, and the situation is getting even worse.

NICK SCHIFRIN: So, those are some of Austin's strongest words about the humanitarian situation in Gaza.

Israeli officials continue to blame the U.N. for a lack of distribution capacity.

And, William, Israeli officials are telling the U.S. tonight that they will have a humanitarian plan before they assault Rafah.

WILLIAM BRANGHAM: Nick, part of these negotiations over the cease-fire and over the release of hostages is also this conversation about how to move those Gazans trapped in Rafah to the north in advance of this assault.

What is the state of those negotiations?

NICK SCHIFRIN: The talks appear to be at an impasse after Prime Minister Benjamin Netanyahu withdrew his negotiators from Doha, where these negotiations take place.

And there appears to be two major disagreements, William.

One is exactly what you just -- we were just talking about, the movement of Gazans from the south to the north.

Israeli officials want to continue to go after Hamas in the north, and they don't want to have to deal with thousands of civilians.

Number two is whether Israeli forces have to withdraw either from the cities or from Gaza itself after the cease-fire.

But the framework of the cease-fire remains.

About 40 hostages would be released in exchange for about 700 Palestinian detainees that Israel has agreed to.

So, the framework still remains, but Netanyahu is calling Hamas' demands delusional.

But, bottom line, U.S. officials tell me these negotiations continue.

WILLIAM BRANGHAM: All right, Nick Schifrin, thank you so much.

NICK SCHIFRIN: Thank you.