Israeli aircraft on Monday began dropping flyers in eastern Rafah, warning thousands of people sheltering in the city that they may be in danger ahead of a possible Israeli operation.

"The IDF will be operating against the terrorist organizations in the area where you are located, as it has operated until now," the flyers read in Arabic, according to a translation provided by the Israel Defense Forces. "Anyone found near terrorist organisations endangers themselves and their family members."

The flyers included directions for an evacuation, including information about the humanitarian area near Al-Mawasi, Israel said.

-ABC News' Joe Simonetti and Kevin Shalvey

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.

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