The pause in hostilities between Israel and Hamas is working, but the Israelis are not going to relent after the attacks that took place in October, as the terrorists will strike again unless they are stopped, Michael Herzog, the Israeli ambassador to the United States, said Sunday. 

"Let me be very clear," Herzog told CNN's "State of the Union." "This is a pause. It is not a cease-fire. Israel cannot and will not allow itself to stop pushing against Hamas following the threat on Oct. 7. We cannot allow ourselves to continue to have Hamas rule Gaza. They will strike again and they will do so."

Hamas, he pointed out, has attacked Israel five times since it took over Gaza in 2007, "so we'll have to continue to dismantle their military infrastructure and their leadership in Gaza, and we'll not stop ... Once we reach the conclusion that they're unwilling to release more hostages, we will resume our operations in Gaza."

Hamas handed over several hostages on Sunday, including a 4-year-old American girl, Abigail Edan, who was kidnapped after she became an orphan while witnessing her parents being murdered by Hamas fighters.

Herzog told CNN that Monday will be the fourth day of the pause, but if Hamas is willing to release more hostages, the pause "could be extended day by day."

"The deal was 50 hostages for the days of pause; and if they produce 10 hostages, they get another day of pause," Herzog said. "That's the deal, and we'll see tomorrow if they are willing to release additional hostages."

Thirty-nine Palestinian prisoners were released Sunday, and the ambassador said Israel will continue to release prisoners as long as Hamas releases the hostages it is holding in Gaza. 

"[Let me] remind everybody that the prisoners that we released are people who were convicted for participating in terror attacks," Herzog said. "They went through a legal process in Israel. We didn't kidnap them. We don't arrest people just for nothing."

Meanwhile, Israel knows at least two American women are being held as hostages, but doesn't know if they will be released in upcoming days, said Herzog. 

"Hamas gives us the list every day for the next day, so we'll see," he said. "I'm hopeful they, too, will be released."

The hostages who have been released are undergoing medical and psychological tests, Herzog added. 

"They were kept in deep tunnels in very bad conditions. So even though they got food and so on, we all understand what it means to be in such a tunnel for dozens of days," he said. "They are being debriefed, and I don't think that's something we want to discuss in public."

Meanwhile, the current hostage release deal pertains only to women and children, so "we'll just have to wait and see" if men will be released, said Herzog. 

Even with the current hostage deal, there will be nearly 200 people still being held by Hamas, he added.

"The families are in pain, and they're anxious. And they expect the government to continue to work for their release," Herzog said. "I will say that all of us in Israel believe that this deal was made possible by our military action in Gaza."

The ambassador added that he does not think Israel's goals of eliminating Hamas while getting the remaining hostages free are contradictory. 

"We strongly believe that this deal was made possible by our military pressure, and that's what we intend to do," said Herzog. "We intend to continue to pressure Hamas in order to get the release of all of our hostages."

Meanwhile, the Palestinian Ministry of Health says more than 14,000 Palestinians have been killed so far including thousands of children, but Herzog said Israel isn't sure if those numbers are true. 

"It's not beyond them to lie about the numbers, and nobody really knows what is the breakdown between innocent civilians and terrorists," he said. "Obviously, there are civilians killed in that war and that's very tragic. It's a tragedy, the loss of every human life; and it is not our intention to hit them."

At the same time, Israel can't "provide Hamas" with immunity "just because they hide behind the civilian population and build an infrastructure of 500 kilometers [310 miles] of tunnel underneath the civilian population," said Herzog. "That's the sad reality we face in Gaza ... We are doing everything to minimize the loss of civilian life. We do not target civilians."

He added that he's urging "everybody to be cautious" with the Hamas numbers, as it is also counting the terrorists who were killed in Israel on Oct. 7. 

"I'm not saying there's no collateral damage. I'm not saying there are no civilian casualties," said Herzog. "There are. This is the unintended consequence of a legitimate war."

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