National Security Council spokesperson John Kirby told reporters that the U.S. is reviewing the Hamas response to a cease-fire proposal.

Kirby did not reveal many specifics about where negotiations stand, but said they’ve reached a “critical stage.”

“I don't know that it gets any more sensitive than right now,” Kirby said. “And the worst thing that we can do start speculating about what's in it.”

-ABC News' Molly Nagle

With negotiations underway for a cease-fire agreement, Israel’s war cabinet said they would continue military operations in Rafah.

Israel will also send a delegation of mediators to work on a possible deal.

There have been at least 50 IDF strikes Monday on Rafah, officials said.

A senior Israeli official with knowledge of negotiations said they have received a response from Hamas on a cease-fire proposal.

It is not the same proposal that had been under discussion, the official said, adding that it will now be studied.

It will take some time before Israel officially responds, the official added.

Israel’s war cabinet is now holding a discussion, according to an Israeli political source.

IDF spokesperson Daniel Hagari said Israel will study every option to bring home hostages, including the latest response from Hamas, and said they would continue operations in the Gaza Strip.

In a statement, the Israeli Hostage Center urged the government to accept the deal. "We welcome the announcement by Hamas to promote the ceasefire, which promotes the return of the 132 abductees who have been held captive by Hamas for 7 months," it said. "Now is the time for the Israeli government to prove in action its commitment to its citizens -- the cabinet must take the consent of Hamas and turn it into a deal for the return of all! The return of the kidnapped is the key to Israeli security!"

-ABC News' Jordana Miller and William Gretsky

The United States said it could confirm Hamas had issued a response to a recent cease-fire proposal, but is still trying to figure out the details of the apparent deal.

"We are reviewing that response now and discussing it with our partners in the region," State Department spokesperson Matthew Miller said at a briefing. "As you know, [CIA] Director [Bill] Burns is in the region working on this in real time. We will be discussing this response with our partners over the coming hours. We continue to believe that they asked them to do what is in the best interest of the Israeli people."

But Miller didn’t suggest the U.S. had a full understanding of exactly what Hamas had agreed to yet.

"We have only received a response in the last hour, 90 minutes," he said. "So I don't want to characterize the nature of that just yet."

Miller also declined to say whether the U.S. believes the military and political factions of Hamas were on the same page.

"I'm just not going to speak for Hamas at all, as we have said for some time, there has been a significant offer on the table. The ball has been in Hamas’ court, we have made clear that they should accept that offer," he said.

-ABC News' Shannon K. Crawford

More than 300,000 people have fled Rafah in the week since Israel issued a partial evacuation order, the United Nations agency operating in Gaza said on Sunday.

The U.N. Agency for Palestine Refugees called the evacuation "forced and inhumane."

"There is nowhere safe to go," the agency said on social media, repeating the phrase three times for emphasis.

The Israeli military late Saturday called again for civilians to evacuate from much of the eastern part of the city, which is in southern Gaza.

Israel Defense Forces entered Rafah last week, in what they called a "precise" operation ahead of potential invasion.

"Prior to our operations we urge civilians to temporarily move towards humanitarian areas and move away from the crossfire that Hamas puts them in," the Israel Defense Forces said on a post on Telegram. "Our war is against Hamas, not against the people of Gaza."

-ABC News' Dragana Jovanovic and Kevin Shalvey