Gen. C.Q. Brown, the chairman of the Joint Chiefs of Staff, said that in meetings in Israel on Monday with senior Israeli political and military leaders, he and Defense Secretary Lloyd Austin will discuss Israel’s criteria for deciding when to transition to stability operations in Gaza at the end of its major military operations and ensuring it is "a smooth transition."

"The goal here is to have better security than they had prior to the events on 7 October," Brown told reporters Sunday while en route to Israel.

Austin and Brown speak regularly with their Israeli counterparts about the conflict with Hamas and urge Israel to protect civilian lives as it carries out its operations, but their trip will build on National Security Advisor Jake Sullivan’s meetings last week in Israel that had a similar focus.

"Part of this is us sharing our own experience and not building a plan for the Israelis, but actually talking through our own experiences and how we've gone through various conflicts in the past," explained Brown.

Brown said the next phase of stability operations in Gaza has to provide
"some level of stability to provide support for security, governance," and the continued flow of humanitarian aid.

He added that senior U.S. military officers can offer political leaders an idea of what will be needed to carry out those stability operations and ensure a smooth transition.

But Brown said he would also be listening to Israel's viewpoint.

"It's more of a dialogue that goes both ways, and I'm trying to understand where they're coming from and what they’re -- how they see things," he said. "And I try to share based on my experience and the things that we see on how best to move forward."

-ABC News’ Luis Martinez

Israel Defense Forces claimed on Sunday that it has discovered one of Hamas' biggest tunnels under the Gaza Strip and that it plans to destroy it.

Measuring nearly 2 1/2 miles long and large enough to drive a vehicle through, the tunnel's entrance was located roughly 1,300 feet from the Erez border crossing between Gaza and Israel, the IDF said in a post on the social media site X.

The shaft, constructed with reinforced concrete and reaching a depth of more than 160 feet, is believed to have taken years to build and millions of dollars to complete, according to the IDF. The tunnel is also equipped with electricity, communications networks and rails, according to the IDF.

It's unclear when the tunnel was found. The IDF said it also found weapons, militants and booby traps in the tunnel.

The tunnel, according to the IDF, is the brainchild of Mohammed Sinwar, the brother of Hamas leader Yahya Sinwar. The IDF released a Hamas video it seized showing Mohammed Sinwar in the passenger seat of a Jeep driving inside the tunnel.

IDF spokesperson Daniel Hagari told reporters that the tunnel would be destroyed.

"Without demolishing the tunnel project of Hamas, we cannot demolish Hamas," Hagari said.

The IDF claims to have destroyed more than 800 tunnels in Gaza since the beginning of the war.

ABC News' Ines De La Cuetara

The Israel Defense Forces commander said the accidental shooting this week of three Israeli hostages in Gaza was "against the rules of engagement."

The three hostages "did everything possible so that we would understand -- they moved around shirtless so that we wouldn't suspect them of carrying explosives and they held a white cloth, but the tension overcame all of the above," Lt. Gen. Herzi Halevi said in a video statement Saturday.

He noted that the shooting of someone who raises a white flag and seeks to surrender "is forbidden."

"However, this shooting was carried out during combat and under pressure," Halevi added. "There may be additional cases in which hostages escape or are abandoned during combat, and we have the duty and responsibility to rescue them alive."

Halevi said he and the IDF are responsible for what happened and "will do everything to prevent such incidents from recurring in future combat."

-ABC News' Dorit Long

Inbar Hayman, an Israeli hostage who was captured at the Re'im music festival, was killed in Hamas captivity, Israeli government spokesperson Eylon Levy said Saturday.

Hayman, 27, ran from the festival with two friends but was caught by "terrorists riding motorcycles," the Hostages and Missing Persons Families Forum said in a statement Saturday.

-ABC News' Dorit Long