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

In a phone call Sunday with his Israeli counterpart, White House National Security Advisor Jake Sullivan expressed an "ironclad U.S. commitment" to Israel but also voiced the Biden administration's concerns about Israel's major military operations in Gaza, according to the White House.

During the call with Israeli National Security Advisor Tzachi Hanegbi, Sullivan reiterated President Joe Biden's "longstanding concerns over the potential for a major military ground operation into Rafah, where over one million people have taken shelter," according to a readout of the call that was released by the White House.

"He [Sullivan] discussed alternative courses of action to ensure the defeat of Hamas everywhere in Gaza," the readout said. "Mr. Hanegbi confirmed that Israel is taking U.S. concerns into account."

The White House said Sullivan also expressed condolences on Israel's Memorial Day, the first since Hamas' surprise Oct. 7 attacks on Israel. The Hamas attack killed 1,200 people, most of them civilians, according to Israel's Prime Minister's Office.

Sullivan and Hanegbi also reviewed discussions by officials on both sides of the war about alternatives for a Rafah invasion and agreed to plan an in-person meeting soon, according to the White House.

-ABC News' Michelle Stoddart