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

Hamas operatives fired "mortar shells" toward the "engineering work area" where Israel Defense Forces troops are conducting preparations for the U.S. military's humanitarian pier near Gaza earlier Wednesday, the IDF said in a response to an inquiry from ABC News.

The U.S. military began building the pier off the coast of Gaza last month to establish a maritime corridor to bring humanitarian aid into Gaza.

-ABC News Dana Savir

More than 300,000 people have fled Rafah in the week since Israel issued a partial evacuation order, the United Nations agency operating in Gaza said on Sunday.

The U.N. Agency for Palestine Refugees called the evacuation "forced and inhumane."

"There is nowhere safe to go," the agency said on social media, repeating the phrase three times for emphasis.

The Israeli military late Saturday called again for civilians to evacuate from much of the eastern part of the city, which is in southern Gaza.

Israel Defense Forces entered Rafah last week, in what they called a "precise" operation ahead of potential invasion.

"Prior to our operations we urge civilians to temporarily move towards humanitarian areas and move away from the crossfire that Hamas puts them in," the Israel Defense Forces said on a post on Telegram. "Our war is against Hamas, not against the people of Gaza."

-ABC News' Dragana Jovanovic and Kevin Shalvey