Israel's insistence on maintaining its ability to operate throughout Gaza against Hamas was a major sticking point in cease-fire negotiations that have fallen through, a senior Israeli official told ABC News.

The official said Israel will have to operate in Rafah, even if a deal is struck. One of the key problems Israel sees with the proposed deal is the demand for an end to the war when Hamas is still "well established" in Rafah.

-ABC News' Will Gretsky

The delegations for Hamas and Israel have left Cairo without a cease-fire deal, Israeli and Egyptian officials said.

Hamas said earlier in the week that they had agreed to a cease-fire proposal, prompting celebration from both sides, but Israel soon after said the deal was not the one it had proposed and included "significant gaps." However, Israel committed to send negotiators to Egypt anyway in hopes of coming to an agreement on a cease-fire deal that would also likely include the release of hostages held in Gaza.

It is unclear when negotiations will resume.

-ABC News' Jordana Miller and Ayat Al-Tawy

As the Israeli military steps up attacks in the southern Gaza enclave of Rafah in preparation for an apparent large-scale incursion, about 80,000 people have now fled, according to the United Nations Relief and Works Agency for Palestine Refugees in the Near East, the U.N. relief agency in Gaza.

"The toll on these families is unbearable. Nowhere is safe," UNRWA said in a post on social media.

About 1.5 million people were living in Rafah recently after Israel directed people in the north to flee south during its initial incursion into the Gaza Strip. The U.S. has warned Israel against a large-scale attack in Rafah unless an evacuation plan can be carried out first.

The first ship carrying aid for Gaza that will be offloaded at the floating military pier assembled off of Gaza has left Cyprus, according to the Pentagon.

The plan is for the aid aboard the M/V Sagamore to be staged onto the military ship M/V Roy P. Benavidez so that it can then be loaded onto trucks at a floating dock and then driven ashore off the floating pier. That dock and pier are fully assembled but are not currently off Gaza.

The dock and pier had to be moved to calmer waters off Ashdod, Israel, but once the mooring point in Gaza stabilizes they’ll be moved into position to begin the opening of the maritime corridor for aid for Gaza.

-ABC News' Luis Martinez and Anne Flaherty

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