Israel-Gaza updates: Police killed in border shooting, authorities say

In an Israeli cabinet meeting, Israeli Prime Minister Benjamin Netanyahu doubled down on his stance that he will not agree to a cease-fire and hostage deal that includes the withdrawal of Israeli troops from the Philadelphi corridor in Gaza, according to an Israeli official.

Israeli troops remaining in the Philadelphi corridor has been a key sticking point in the ongoing negotiations. Hamas wants a complete withdrawal of Israeli troops from Gaza.

"Everyone who says that it is possible to leave Philadelphi for 42 days, knows very well that it will be for 42 years. The world will not allow us to return," Netanyahu said during Sunday night’s cabinet meeting, according to an Israeli official. "Everyone understands the importance of Philadelphi, and [Hamas leader Yahya] Sinwar understands it best. That is why he insists. All smuggling the weapons to Gaza were through Philadelphi. If we change the cabinet's decision, it will be a terrorist award, you will not return the hostages."

The Hostages Families Forum said in a statement that Netanyahu’s comments are "dangerous." The families said Netanyahu's statement means "there will be no deal, and the families will not get to see their loved ones return home."

-ABC News’ Jordana Miller and Dana Savir

As Israeli President Isaac Herzog gave a eulogy at the funeral of Israeli-American hostage Hersh Goldberg-Polin, he apologized to the slain 23-year-old.

"I apologize that the country you immigrated to at the age of 7, wrapped in the Israeli flag, could not keep you safe," Herzog said Monday, two days after the Israeli-American's body was recovered in Gaza, along with five others.

The president also asked for forgiveness from Goldberg-Polin's parents, Rachel Goldberg-Polin and Jon Polin, for not bringing their son home alive.

He said he learned of "a mother's and father's limitless love" from Rachel Goldberg-Polin and Jon Polin.

"Jon and Rachel, against the senseless hatred, and unthinkable brutality of Hamas terror, pure barbaric evil, you have taught the world about human dignity," Herzog said. "As a human being, as a father, and as the President of the State of Israel, I want to say how sorry I am. How sorry I am that we didn’t protect Hersh on that dark day. How sorry I am that we failed to bring him home."

Though he said Israel will "continue fighting relentlessly against" Hamas, Herzog stressed that the remaining 97 hostages must be released.

"The time to act is now: Bring them home," Herzog said.

"Decision-makers must do everything possible, with determination and courage, to save those who can still be saved," he said. "This is not a political goal, and it must not become a political dispute. It is a supreme moral, Jewish, and human duty of the State of Israel to its citizens."

-ABC News’ Becky Perlow

When asked by reporters if Israeli Prime Minister Benjamin Netanyahu is doing enough on the hostage deal, President Joe Biden on Monday replied, "No."

Asked about presenting a final hostage deal this week, Biden said, "We are very close to that."

"Hope springs eternal," Biden said, when asked what makes this final deal different, but he declined to provide details.

Biden and Vice President Kamala Harris are meeting with the U.S. hostage negotiation team Monday morning.

Click here to read more.

-ABC News’ Lauren Peller

Hersh Goldberg-Polin’s mother, Rachel, spoke directly to her slain son at his funeral Monday, saying she had been "absolutely certain that you were coming home to us alive. But it was not to be."

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Mom of slain hostage asks her son to 'help us to rise again'

Hersh Goldberg-Polin’s mother, Rachel, spoke directly to her slain son at his funeral Monday, saying she had been "absolutely certain that you were coming home to us alive. But it was not to be."

ABCNews.com

"Now I no longer have to worry about you. I know you are no longer in danger," she said. "But now my worry shifts to us. ... How do we live the rest of our life without you?"

Rachel Goldberg-Polin said she had always dreamed of what kind of man her 23-year-old son would grow up to be, but now he will always stay her energetic, kind, patient, funny and pensive "sweet boy."

"If there was something we could’ve done to save you and I didn’t think of it, I beg your forgiveness," she said to her son, days after his body and the body of five other hostages were recovered in Gaza.

She also asked for her son’s help "as we transform our hope into grief in this new, unknown brand of pain."

"I beg of you, Hersh, please do what you can … help shower us with healing and resilience. Help us to rise again," she said.

She said she hopes one day that their family -- including Hersh’s dad and two sisters -- will "hear laughter and turn around -- and see it’s us and were OK."

Through tears, the grieving mom begged her friends to help the family through this "sickening new chapter," pleading, "please don’t leave us now."

To her son, she said, "Finally, you're free. ... I love you and I will miss you every single day for the rest of my life."