The Jordanian government released a readout of the meeting between King Abdullah II and Secretary of State Antony Blinken on Tuesday.

Abdullah "warned of the danger of any military operation in Rafah, stressing that the catastrophic effects of the war in Gaza could spread to areas in the West Bank, Jerusalem, and the entire region," according to the readout.

The king also called for more aid to Gaza "through all available means," the readout said.

"The King said supporting UNRWA is crucial to enable it to cover the basic needs of nearly 2 million Palestinians in Gaza, as well as other Palestinian refugees in its areas of operation," the readout said.

The U.S. and some other countries pulled funding for UNRWA, the United Nations Relief and Works Agency for Palestine Refugees in the Near East, after Israel said several staffers took part in Hamas' Oct. 7 attack.

-ABC News' Cindy Smith

Israel will not send a delegation to Cairo for negotiations on a cease-fire deal until Hamas provides an answer to the proposal Israel has offered them, an Israeli source told ABC News.

-ABC News' Jordana Miller

White House national security spokesman John Kirby declined to comment about Israeli Prime Minister Benjamin Netanyahu's latest comments about a possible operation into Rafah during a news conference Tuesday.

"Our position on Rafah is absolutely the same. We don't want to see a major ground operation in Rafah. Certainly, we don't want to see operations that haven't factored in the safety and security of those 1.5 million folks trying to seek refuge down there," Kirby said.

He also declined to say if Netanyahu has shared his plans to enter Rafah with or without a deal directly with the United States.

"They understand our concerns, and those concerns have not changed," he said, adding that they have not seen a credible plan yet from Israel to take civilian safety into consideration though conversations continue.

Kirby reiterated that the new cease-fire deal is on the table, which would give a six-week pause in fighting and help get the hostages home.

Kirby downplayed expectations, but stressed "time is of the essence."

"I wouldn't say we're overly confident. I would say we're being very pragmatic about this," he said.

-ABC News' Molly Nagle

Israeli Prime Minister Benjamin Netanyahu said an operation in Rafah will proceed in comments Tuesday.

"We will enter Rafah because we have no other choice," Netanyahu said in comments translated from Hebrew. "We will destroy the Hamas battalions there, we will complete all the objectives of the war, including the repatriation of all our hostages."

No timeline has been given for a military operation in Rafah, where over 1 million refugees have gathered in the wake of Israel's bombardment of the Gaza Strip.

The prime minister also criticized the International Criminal Court, saying it "has no authority over the state of Israel." The ICC is currently investigating Israel's actions in Gaza, as well as the Oct. 7 Hamas attack on Israel that launched the Israeli response.

"The possibility that it will issue arrest warrants for war crimes against IDF commanders and state leaders, this possibility is a scandal on a historical scale," Netanyahu said.

He added, "I want to make one thing clear: no decision, neither in The Hague nor anywhere else, will harm our determination to achieve all the goals of the war."

-ABC News' Jordana Miller

Osama Hamdan, a senior Hamas official, said in a statement that cease-fire negotiations with Israel will cease if it moves forward with its operation into Rafah.

"The Israeli enemy is trying to blackmail everyone with the Battle of Rafah," he said in a statement.

Hamdan told Lebanese TV late Wednesday that a cease-fire deal had not been reached and Hamas was still "studying the swap deal proposal."

"We have substantial notes on the proposal," Hamdan told Lebanese TV.

"We are studying the proposal and we will respond to it in a way that serves our goals."

-ABC News' Dia Ostaz, Ellie Kaufman and Ghazi Balkiz