U.S. officials shared an update Thursday on efforts to bring aid into Gaza through the Army's Joint Logistics Over-the-Shore (JLOTS) system, a floating pier built to transport aid to the region.

Since Friday, over 506 metric tons of aid have been transported via the pier, according to officials.

Officials from U.S. Central Command (CENTCOM) and the U.S. Agency for International Development (USAID) held an audio-only briefing with reporters on continued aid efforts.

"Since the first shipments of this aid arrived through the humanitarian maritime corridor on Friday, the UN has been distributing more than 506 metric tons of humanitarian supplies to people in need," Daniel Dieckhaus, Director for USAID’s Levant Response Management Team, said Thursday.

"To put it into perspective, more than two thirds of the supplies entering through this new corridor have already been distributed, or are in the process of being distributed by humanitarian partners directly to people in need," he added.

Humanitarian aid has also been delivered through land-crossing distribution via 70 trucks that crossed the border into Gaza, according to Dieckhaus.

Vice Admiral Brad Cooper, deputy commander of CENTCOM, noted that, "In the last several days, we've delivered over a million pounds of aid into the hands of Palestinians," adding, "We can all feel good about that."

President Joe Biden refused to say whether the U.S. has any evidence that would support the International Criminal Court prosecutor’s allegation that Israeli leaders are using starvation as a method of war in Gaza.

Biden was asked if that evidence exists and if the administration would commit to releasing that information before any warrants are issued, but he only reiterated that the U.S. does not recognize their jurisdiction.

"We've made our position clear on the ICC. We don't recognize their jurisdiction -- the ICC, the way it's being exercised -- and it's that simple. We don't think there's an equivalence between what Israel did, and what Hamas did," Biden said.

-ABC News' Justin Ryan Gomez

Israeli Defense Forces are now fighting near central Rafah, representing an expansion of its operations, the IDF said Thursday.

Close to 1 million people have been evacuated from Rafah, according to IDF Commanding Officer Daniel Hagari.

-ABC News' Will Gretsky

The Egyptian government said Wednesday that attempts to undermine its efforts to broker a Gaza cease-fire deal could push it to entirely pull out of mediation in the conflict.

Diaa Rashwan, the head of Egypt’s State Information Services, said Egypt categorically rejected a report from CNN that claimed his government changed the terms of a Gaza cease-fire deal that Israel had already signed off on before submitting it to Hamas.

Rashwan called the report "false" and "devoid of any information or facts."

"The ongoing attempts to cast doubt and insult the Egyptian mediation efforts and roles, with allegations that contradict reality, will only lead to further complicating the situation in Gaza and the entire region, and may push the Egyptian side to take a decision to withdraw completely from the mediation it is carrying out in the current conflict," he said in a statement.

Rashwan added that Egypt would only open the Rafah border crossing if the Palestinian side is operated by Palestinians, reiterating that Cairo does not acknowledge the Israeli control of the Palestinian side of the crossing.

-ABC News' Will Gretsky

President Joe Biden secured a commitment from Egypt in a discussion Friday with Egyptian President Abdel Fattah El-Sisi to resume deliveries of U.N. aid into Gaza through the Kerem Shalom crossing, according to a White House readout of their call.

Biden also expressed his support to reopen the Rafah crossing with "arrangements acceptable to both Egypt and Israel and agreed to send a senior team to Cairo next week for further discussions."

"The two leaders agreed to deliver quantities of humanitarian aid and fuel to the United Nations at the Kerem Shalom crossing. This is temporary until a legal mechanism is reached to reopen the Rafah crossing from the Palestinian side," the Egyptian presidency said.

Aid delivery through the Rafah crossing stopped after Israel stepped up its military offensive in southern Gaza and took control of the crossing on the Palestinian side on May 7.

The leaders also discussed "new initiatives" to reach a deal to secure the release of hostages being held by Hamas and a cease-fire in Gaza. No specifics were provided.

"President Biden and President Al-Sisi affirmed their commitment to work together to set the conditions for a durable and sustainable peace in the Middle East region," the White House said. "They agreed to remain in regular contact both directly and through their senior national security teams."

-ABC News' Justin Ryan Gomez and Ayat Al-Tawy