Almost 360,000 people have fled from the southern Gazan city of Rafah since Israel issued an evacuation order last week, the United Nations agency operating in Gaza said on Monday.

"There's nowhere to go," the U.N. Agency for Palestine Refugees said on social media. "There's NO safety without a cease-fire."

The agency had said Sunday that 300,000 people had evacuated the city as Israel weighs a full-scale invasion.

-ABC News' Kevin Shalvey

The Israel Defense Forces has announced that it has opened a new crossing to bring humanitarian aid into the famine-stricken Gaza.

The military announced in a Sunday press release the opening of the Western Erez crossing between Israel and northern Gaza in coordination with the U.S.

According to the military, the new crossing is located west of the Erez crossing, closer to the seashore. The crossing was constructed by the Israeli military "as part of the effort to increase routes for aid to Gaza, particularly to the North of the strip."

Earlier Sunday, IDF said it launched a large-scale operation in the area of Jabaliya in the North, while intensifying its military operations in the Eastern portion of Rafah and the Gaza side of the Rafah crossing. It said that it had called on the civilian population to evacuate from Jabaliya to shelters in the west part of Gaza City.

-ABC News' Dragana Jovanovic

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

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

Israel announced that it has identified the body of a fourth hostage this week. Ron Benjamin, 53, was killed during the Oct. 7 Hamas attack and taken into Gaza, according to the Israel Defense Forces.

The bodies of three other hostages were also recovered in a tunnel in the same operation, according to the IDF.

Benjamin was a family man who loved cycling, the Hostages Families Forum said in a statement.

"He used to go out for a ride every Saturday, just as he did on that fateful Saturday when he was taken hostage from the Kibbutz Be’eri area while on a cycling trip," the statement said.

-ABC News' Victoria Beaule