AMNA NAWAZ: The negotiations that led to the Hamas-Israel cease-fire agreement took months and months.

In the room and at the center of the talks representing the United States was Brett McGurk, White House coordinator for the Middle East and North Africa.

He joins me now.

Brett, welcome to the "News Hour."

Thanks for being with us.

BRETT MCGURK, White House Coordinator For the Middle East and North Africa: Amna, thanks so much for having me.

AMNA NAWAZ: So you have been on the front lines of these efforts to end this war.

Take us inside the negotiations, if you can.

At any point over the last several months did you just worry you were never going to get to a deal?

BRETT MCGURK: The president laid out this framework in May, at the end of may, and the Israelis agreed to it.

And in August, we actually thought we were getting close to a deal.

The U.S., Egypt, and Qatar, we put together what we called a mediator proposal to try to bridge some differences.

I have to say Hamas never accepted the deal.

Hamas never agreed to release hostages, other than solely on its terms, which was basically for the Israeli forces to totally leave Gaza, permanent cease-fire, and go back to October 6, kind of bygones be bygones.

And no Israeli government was going to do that.

And then we had six hostages killed in a tunnel underneath Southern Gaza, underneath Rafah, including an American Hersh Goldberg.

And we pretty much concluded that, with the current leadership of Hamas, and given the regional situation at the time, in which Hamas believed that a multifront war that had been opened up against Israel with the behest of Iran, it was not going to do a deal.

So we had to change the equation, and that's really what we did.

Of course, Israel began its campaign in Lebanon.

That's actually been quite successful.

That removed this threat from Hezbollah, and it isolated Hamas really for the first time.

And, of course, the leader of Hamas, Yahya Sinwar, was killed in Gaza around the same time, and that also removed a critical obstacle.

So, December, after the Lebanon cease-fire, is when we reengaged very intensively.

AMNA NAWAZ: There was a lot of attention paid, of course, to the unprecedented coordination between the outgoing Biden administration and the incoming Trump team, specifically between you and Mr. Trump's envoy Steve Witkoff.

How did that work?

I mean, how do you represent two leaders with very different approaches, very different world views towards the same goal?

BRETT MCGURK: Well, yes, I think it's historic.

I think it's effective.

Steve became a close partner of mine, I think it's safe to say a friend.

Shortly after the election, remember, president-elect Trump came to see President Biden in the Oval Office, and President Biden set the tone.

Look, we're going to have a seamless transition, and we're going to try to work together where we can.

And I spent most of the last six weeks, first in Cairo, then in Doha, kind of nailing this down.

And it was at the end of December, Amna.

This is a critical point.

It was at the end of December.

For the first time, for the first time in a year, Hamas agreed to a list of hostages that it was prepared to release in the first phase of a deal over six weeks.

And after that happened -- and they had not done that until that point -- we were then in the bargaining to try to close it, what is the exchange, Palestinian prisoners for hostages, some details of the cease-fire, the redeployment of Israeli forces?

And we were really kind of then in the stages that we thought we could actually get this done.

AMNA NAWAZ: Brett, this deadline, of course, with the incoming administration, we saw previously president-elect Trump had threatened that there would be hell to pay if the hostages weren't released by the time he was sworn in on January 20.

What do you believe would have happened if the hostages weren't released by inauguration or aren't released, if the deal wasn't done?

Would the war have escalated?

BRETT MCGURK: Well, first of all, I mean, I think there has been hell to pay.

And looking back now 18 months, I think those who decided that was an opportune moment to launch a war against Israel have paid a very heavy price.

Look, this deal is difficult.

Any deal like this is difficult.

I have done a few of them, nothing kind of this dimension.

But, for Israel, it's difficult.

Many Palestinian prisoners, many Hamas prisoners will be released under the steel.

And the Israeli government is debating it now as we speak, and going on hours, because it's a complex deal.

And they should debate it and they should approve it.

I'm very confident they will.

AMNA NAWAZ: President Biden has spoken about this deal since it was announced.

In an interview just last night, he said that, within the first 10 days of the war, he shared this for the first time, that he met with Netanyahu, and he told him back then -- quote -- "You can't be carpet-bombing these communities."

He said, Netanyahu said back to him, "Well, you did it," referring to the U.S. bombing in World War II and the U.S. nuclear bombing in Japan, in other words, justifying the mass civilian casualties to come.

BRETT MCGURK: The discussions in those early days was about the extreme difficulty of an enemy that has hundreds of miles of tunnels underground and a civilian population that, of course, is not allowed in those tunnels, and that has nowhere to go.

And how do you do this?

AMNA NAWAZ: For now, at more than 46,000 Palestinians dead, the vast majority of them women and children, I guess the question now left for the U.S. to answer, is that proportionate?

Were those 46,000 deaths proportionate for the attacks on October 7?

BRETT MCGURK: Well, we just negotiated a cease-fire, ultimately, we hope, if it goes through all three phases, that ends the war.

And the only way to end the war was a hostage deal.

AMNA NAWAZ: Hamas has reneged before, even attempted to in the last few days.

We know Mr. Netanyahu is still under pressure back in Israel from a part of his government that doesn't want this deal.

How tenuous is this cease-fire?

BRETT MCGURK: We worked tirelessly to nail down literally every single conceivable detail, every Palestinian prisoner that will be released, the rules of the road for the cease-fire, exactly where Israeli forces will be and won't be, what Hamas can do, what they can't do, all the provisions for humanitarian aid.

So it is all outlined.

It is clear what all the parties need to do.

I think this deal has broad support amongst the Israeli people, and, of course, the Gazans who have been living in hell.

We have said that multiple times.

This will bring relief, needed relief, finally, a cease-fire, a surgeon aid and stopping the war.

AMNA NAWAZ: Brett McGurk, White House coordinator for the Middle East and North Africa.

Thank you so much for joining us, Brett.

Good to speak with you.

BRETT MCGURK: Amna, thank you so much.

AMNA NAWAZ: And just moments ago, after I spoke with Brett McGurk, we received word that Israel's Cabinet has now approved the cease-fire agreement.