Ismail Haniyeh, head of the political bureau of the Hamas movement, said in a statement the group has called the prime minister of Qatar and Egyptian minister of intelligence "and informed them of the Hamas movement's approval of their proposal regarding the ceasefire agreement."

While few specifics were provided, senior Hamas leader Taher Al-Nono said the proposal "includes a ceasefire, reconstruction, the return of the displaced, and the liberation of prisoners."

Al-Nono said representatives would visit Cairo in the near future to discuss the agreement.

A deal has not been confirmed or commented on by other parties, including Israel. ABC News has requested comment from Israel, Qatar, Egypt and the U.S. on the apparent agreement.

-ABC News' Nasser Atta

The Pentagon said it still hasn’t seen a "credible" plan from Israel on how it will protect some 1 million civilians in Rafah in the case of an invasion.

"We've seen kind of a concept, but nothing detailed at this point," Pentagon press secretary Maj. Gen. Pat Ryder told reporters Monday morning.

He noted that the subject was raised Sunday by Defense Secretary Lloyd Austin in a phone call with Israel's defense minister, Yoav Gallant, but he declined to say what policy changes the U.S. might consider if Israel begins a full-scale invasion of Rafah without that credible plan.

Austin is scheduled to testify Wednesday, the same day the administration is required by law to tell Congress whether it agrees with Israel that its government complies with humanitarian law.

"I think there are still concerns in terms of the, again, given the number of people there and how you're going to take into account the safety and well-being of the million-plus people that are in Rafah as any operation commences," Ryder said. "Again, we agree with our Israeli partners on the importance of defeating Hamas and preventing them from being able to conduct attacks like they've done in the past. But we want to see that operation done in a way that again, takes into account civilians, takes into account how you're going to evacuate them off the battlefield. So those conversations will continue."

-ABC News' Anne Flaherty

President Joe Biden spoke with Israeli Prime Minister Benjamin Netanyahu on Monday, a source confirmed to ABC News.

Biden was expected to again reiterate his position on Rafah, urging restraint when it comes to an invasion of the enclave holding more than 1 million Gaza refugees, as he did when they last spoke on April 28.

Click here to read more about the conversation.

-ABC News' Mary Bruce and Justin Gomez

Israeli military jets targeted areas of Rafah overnight, striking "terror targets" and military structures, including a sniper's nest, the Israel Defense Forces said Monday.

The strike included areas of Rafah "from which projectiles were launched toward the area of Kerem Shalom yesterday," IDF officials said on Telegram.

There were no immediate reports of injuries following Monday's strikes. IDF strikes on Sunday had killed at least 12 people in Rafah.

-ABC News' Kevin Shalvey and Joe Simonetti