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

Although the Biden administration said it expected the Kerem Shalom and Rafah gates to be at least partially opened for humanitarian aid by Wednesday, the State Department was much less optimistic. However, the U.S. vowed it would continue to press Israel to get both portals up and running again.

While Kerem Shalom reopened Wednesday, aid had not been allowed to pass through because of "logistical and security concerns on the ground," State Department spokesperson Matt Miller said during a briefing Wednesday. He also said fuel had not been able to enter Gaza through Rafah.

"We think it's critical that Rafah be open for fuel because without fuel deliveries into Rafah, humanitarian assistance that comes in through Kerem Shalom can't actually be delivered. The two are critically linked," Miller said. "We're continuing to push for that to happen."

Miller didn’t provide any updated timeline on when the U.S. expected the crossings would be functional again, but said it was imperative that Israel act to increase the amount of aid allowed into Gaza following what he described as a "fairly dramatic dip" this week.

"When it comes to the level of humanitarian assistance, the results as they are today are just unacceptable. There's no other way to put it," Miller lamented.

He continued, "We are making quite clear to the government of Israel that we need to see those decreases reversed. We need to get back to where we were, and we need to see the levels continue to increase and see those sustained, and that is why we need to see Kerem Shalom and Rafah opened."

-ABC News' Shannon Crawford