AMNA NAWAZ: Welcome to the "NewsHour."

Delegations from Israel and Hamas returned to Cairo to resume fraught negotiations over a potential cease-fire and hostage deal.

In the meantime, Israeli tanks and troops seized the Rafah border crossing with Egypt, delaying aid shipments, as 1.2 million Palestinians shelter in the city.

Following it all is our Nick Schifrin, reporting tonight from Jacksonville, North Carolina.

So, Nick, let's begin in Rafah.

Tell us what kind of operation Israel has launched there and why.

NICK SCHIFRIN: Well, Amna, as you just said, Israel sees the border crossing that separates Gaza from Egypt.

Israel called it a -- quote - - "precise operation" to tackle some of the smuggling that goes from Egypt into Gaza, as well as the Hamas militants who operate there.

This is actually the first time that Israeli troops have controlled that border crossing since 2005, when Israel withdrew settlers and soldiers from Gaza back then.

And in this war, Israel has long argued that it needs to enter nearby Rafah City.

And, today, Israeli Prime Minister Benjamin Netanyahu said that operation was next.

BENJAMIN NETANYAHU, Israeli Prime Minister (through translator): Seizing the passage in Rafah today is a very important step, an important step on the way to destroying the remaining military capabilities of Hamas, including the elimination of the four terrorist battalions in Rafah, and an important step to damage the governmental capabilities of Hamas, because, as of this morning, we denied Hamas a passage that was essential for establishing its reign of terror in the strip.

NICK SCHIFRIN: But Rafah is also the main crossing of humanitarian aid from Egypt into Gaza.

And, today, hundreds of trucks are backed up at the border because the crossing is shut, as is the nearby crossing of Kerem Shalom, which Israel promised to open by tomorrow.

And the U.N. warned today that food and fuel to Southern Gaza will run out by the end of the week.

And, of course, Amna, as you and I have talked about so often, the U.N. is warning that famine is imminent.

AMNA NAWAZ: Nick, help us understand now.

Both sides are -- also seem to be making clear today that this operation is intertwined with the fate of those hostage negotiations as well.

Is that right?

NICK SCHIFRIN: It's certainly what Israel has said, Amna, absolutely, that Israel has said that this military operation must continue in order to keep the pressure on Hamas, so that Hamas agrees to the latest version of the hostage negotiation deal.

But the fact is right now that the ball is in Israel's court.

Hamas submitted a new to the latest version of the hostage negotiation deal.

Israeli officials said that Hamas had actually created new versions or new aspects of that deal.

And a senior U.S. official today confirmed to me that the Hamas changes were significant.

But, still, the U.S. is hoping that progress can be made.

John Kirby, the National Security Council spokesman, saying today that the two sides should be able to -- quote -- "close the gaps."

But, today, Hamas, spokesman Osama Hamdan warned that a major Rafah operation means no deal over hostages.

OSAMA HAMDAN, Hamas Spokesperson (through translator): If the aggression continues, there will be no cease-fire, because Israelis are the ones attacking and shooting.

It is normal for the resistance to respond to this aggression, to respond in defense, and to respond in order to defeat the occupation.

NICK SCHIFRIN: Now, this is all part of the diplomacy that CIA Director Bill Burns has been leading, and his trip to the region continues today.

The U.S. is pressuring Netanyahu to make the deal, as are the families of hostages being kept in Gaza.

And the U.S. has also pushed Qatar to threaten Hamas with expulsion from Doha, where the political leadership of Hamas is based if Hamas rejects this deal.

It's not clear, Amna, if this deal can be made.

But the U.S. knows it is urgent.

U.S. officials tell me that Israel has imposed a deadline by the end of the week and then, if this deal is not set by then, it will launch that major operation into Rafah, defense Minister Yoav Gallant making that explicit today.

He said, if there's no deal, Israel will -- quote -- "go deeper into Rafah."

AMNA NAWAZ: That is Nick Schifrin reporting tonight from Jacksonville, North Carolina.

Nick, thank you.