Israel-Gaza updates: 300,000 have fled Rafah, UN agency says

As cease-fire talks continue, IDF spokesperson Daniel Hagari again warned Palestinians in the eastern part of the city to evacuate.

"Tonight, we also call upon those staying in specific areas which we have communicated and defined through every means -- radio, media, internet, and flyers -- in eastern Rafah, to move towards the expanded humanitarian area in Al-Mawasi and Khan Yunis, where they will receive full humanitarian aid and where water, food, medical equipment, and shelter will be provided,” Hagari said.

Israeli Minister Benny Gantz said in a statement Monday the current proposal put forth by Hamas "has significant gaps.”

"Despite this, we continue to turn over every stone and a delegation will go to Cairo," he added.

Gantz said “every decision will be brought to the war cabinet,” which is made up of Israeli Prime Minister Benjamin Netanyahu, Israeli Defense Minister Yoav Gallant and himself.

-ABC News' Dana Savir

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.