Israel-Gaza live updates: US official says 2 sticking points in cease-fire deal

Far-right National Security Minister Itamar Ben-Gvir said he is "working to stop the negotiations with Hamas," as talks over a cease-fire and hostage release deal continue under massive public and international pressure.

Ben-Gvir -- one of the most vocally hawkish members of Prime Minister Benjamin Netanyahu's government -- wrote on X that Israel should end negotiations and cut fuel and electricity to Gaza in response to Hamas' recent killing of six hostages in the southern strip.

"Continuing the negotiations only spurs them to produce more and more terror," including in the West Bank, Ben-Gvir said.

Ben-Gvir is a longstanding proponent of expanding Israeli settlements in the West Bank. He has called on the government to "encourage" Israelis to settle in Gaza while suggesting "voluntary emigration" of Palestinians from the territory.

Ben-Gvir was convicted of incitement to racism and supporting a terror organization in 2008, related to an anti-Arab placard he displayed at a protest following a Palestinian terrorist attack in Jerusalem. Signs referring to the far-right Kach movement -- a Jewish group banned as a terror organization -- were also found in his car.

-ABC News' Guy Davies and David Brennan

Second gentleman Doug Emhoff said Tuesday night that the parents of Oct. 7 hostage Hersh Goldberg-Polin, who the Israeli military found had been killed last week, do not want their son's "death to be in vain."

Emhoff opened up about the recent conversation he and his wife, Vice President Kamala Harris, had with the couple after learning of the death of their son.

Speaking at a vigil hosted at the Adas Israel Congregation synagogue in Washington, D.C., which was organized to honor the memory of the six Israeli hostages found killed by Hamas in Gaza, Emhoff said Rachel Goldberg-Polin and Jon Polin remained committed to seeing the remaining hostages released.

"And yet, with this unspeakable tragedy that they were going through … they were comforting us, but also asking about the latest in the negotiations," Emhoff told those gathered at the vigil about the call with the grieving couple, which occurred last week. "They were asking how we can use this terrible moment to make progress on the deal. And they told the vice president, in no uncertain terms, they do not want Hersh's death to be in vain. And they spoke with such grace, such compassion, such strength. And even though part of Rachel and Jon's world had just ended, they were somehow still looking forward and looking out for others."

-ABC News’ Oren Oppenheim

The Justice Department unsealed charges Tuesday targeting multiple senior members of Hamas' leadership for their alleged involvement in the kidnapping and murdering of Americans during the Oct. 7 attack.

The criminal complaint, unsealed in the Southern District of New York, names six members of Hamas' leadership structure and details extensively their terrorist activities on behalf of the group.

Click here to read more.

-ABC News’ Alexander Mallin

The White House is pushing back on Israeli Prime Minister Benjamin Netanyahu’s stance of keeping Israeli troops along the Philadelphi corridor -- a narrow strip of land on the Gaza side of the Gaza-Egypt border -- saying the prime minister originally agreed to removing troops in the Israel-approved framework that was announced in May.

“I'm not going to get into a debate with the prime minister and what he said over the weekend about the Philadelphi corridor," White House national security communications adviser John Kirby said. "The deal itself, the proposal, including the bridging proposal that we started working with … included the removal of Israeli Defense Forces from all densely populated areas, and that includes those areas along that corridor. That's the proposal that Israel had agreed to."

Kirby acknowledged Israel’s belief that they need "some security" along the corridor, but Kirby did not give the U.S. position on whether the administration supports the IDF remaining in less dense areas along the border.

"The proposal says that they have to remove themselves to the east from densely populated areas -- and that core essential element of the proposal has not changed," Kirby said. "But the Israelis have said publicly that they believe that … they would need some security along that corridor."

-ABC News’ Justin Ryan Gomez