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

A new report from the United States Departments of State and Defense said that given "Israel's significant reliance on U.S.-made defense articles" it is "reasonable to assess" that some have been used in instances "inconsistent" with Israel's obligation under international law.

The assessment, which came as part of a report ordered by President Joe Biden, examined the use of U.S.-supplied arms in active conflict zones, and also said that the U.S. could not compile enough evidence to prove that the country used American defense articles in violation of international humanitarian law.

"We do not have complete information to verify whether US defense articles covered under NSM-20 were specifically used in actions that have been alleged as violations of IHL (international humanitarian law) or international human rights law during the period of the report," the document says. "The nature of the conflict in Gaza makes it difficult to address or reach conclusive findings on individual incidents."

While the report said the Israeli government has "the knowledge, experience, and tools" to implement "best practices for mitigating civilian harm," the high number of civilian casualties "raise substantial questions about whether the IDF is using them effectively in all cases."

Additionally, the report noted that Israel did not cooperate with U.S. efforts to ramp up humanitarian aid and distribution in Gaza during the initial months of the conflict, but that officials have observed improvements.

-ABC News' Shannon Crawford and Anne Flaherty