The U.N. Agency for Palestine Refugees said Monday it wouldn't begin to evacuate its staff from Rafah, adding that a possible Israeli invasion into the refugee city would be "devastating."

"UNRWA is not evacuating: the Agency will maintain a presence in Rafah as long as possible & will continue providing lifesaving aid to people," the group said in a statement.

An invasion into the city "would mean more civilian suffering & deaths," the agency said.

-ABC News' Kevin Shalvey

Israeli military officials on Monday issued a warning to civilians in eastern Rafah to begin a "gradual movement" to a humanitarian area.

"Calls to temporarily move to the humanitarian area will be conveyed through flyers, SMS messages, phone calls and media broadcasts in Arabic," Israel Defense Forces officials said in a statement posted to social media.

Israel said a humanitarian area around Al-Mawasi, a coastal town, had been expanded "to accommodate the increased levels of aid flowing into Gaza." That aid included new field hospitals and additional food and water, IDF officials said.

Prime Minister Benjamin Netanyahu had said last week that Israel would call for an evacuation of civilians prior to beginning its planned invasion into the southern Gaza city. Israeli officials haven't yet detailed a timeline for the expected operation.

"The IDF will continue pursuing Hamas everywhere in Gaza until all the hostages that they're holding in captivity are back home," IDF officials said Monday.

-ABC News' Kevin Shalvey

Hamas said Sunday that negotiations in Cairo have concluded and that its delegation will leave Cairo tonight.

Although the Biden administration said it expected the Kerem Shalom and Rafah gates to be at least partially opened for humanitarian aid by Wednesday, the State Department was much less optimistic. However, the U.S. vowed it would continue to press Israel to get both portals up and running again.

While Kerem Shalom reopened Wednesday, aid had not been allowed to pass through because of "logistical and security concerns on the ground," State Department spokesperson Matt Miller said during a briefing Wednesday. He also said fuel had not been able to enter Gaza through Rafah.

"We think it's critical that Rafah be open for fuel because without fuel deliveries into Rafah, humanitarian assistance that comes in through Kerem Shalom can't actually be delivered. The two are critically linked," Miller said. "We're continuing to push for that to happen."

Miller didn’t provide any updated timeline on when the U.S. expected the crossings would be functional again, but said it was imperative that Israel act to increase the amount of aid allowed into Gaza following what he described as a "fairly dramatic dip" this week.

"When it comes to the level of humanitarian assistance, the results as they are today are just unacceptable. There's no other way to put it," Miller lamented.

He continued, "We are making quite clear to the government of Israel that we need to see those decreases reversed. We need to get back to where we were, and we need to see the levels continue to increase and see those sustained, and that is why we need to see Kerem Shalom and Rafah opened."

-ABC News' Shannon Crawford