President Donald Trump speaks with Jordan's King Abdullah II in the Oval Office at the White House. AP
"I think one of the things that we can do right away is take 2,000 children, cancer children who are in a very ill state, that is possible," Abdullah said as Trump welcomed him and Crown Prince Hussein in the Oval Office.
Trump called it a "beautiful gesture" and said he didn't know about it before the Jordanian monarch's arrival at the White House.
The US president meanwhile backed down on a suggestion that he could withhold aid for Jordan and Egypt if they refused to take in more than two million Palestinians from Gaza.
"I think we'll do something. I don't have to threaten that, I do believe we're above that," Trump said.
Trump stunned the world when he announced a proposal last week for the United States to "take over" Gaza, envisioning rebuilding the devastated territory into the "Riviera of the Middle East" -- but only after resettling Palestinians elsewhere, with no plan for them ever to return.
Jordan's Abdullah was repeatedly pressed by reporters on whether he supported the plan but said only that Egypt was coming up with a response and that Arab nations would then discuss it at talks in Riyadh.
"The president is looking at Egypt coming to present their plan... (then) we will be in Saudi Arabia to discuss how we should work with the president and with the United States," Abdullah said.
"The point is, how do we make this work in a way that is good for everybody."
The meeting came as the Gaza ceasefire appears increasingly fragile after Trump warned on Monday that "all hell" would break out if Hamas fails to release all captives by Saturday.
Israeli Prime Minister Benjamin Netanyahu on Tuesday said Israel would resume "intense fighting" in Gaza if Hamas did not meet the deadline.
Trump said he doubted that the Palestinian group would abide by the ultimatum.
"I don't think they're going to make the deadline personally. I think they want to play a tough guy, but we'll see how tough they are," Trump said.
But he played down the risk of a longer threat to efforts to create a lasting peace between Israel and Hamas.
"It's not going to take a long time when you know bullies," he added, referring to Hamas.
The Jordanian king and crown prince earlier met Trump's National Security Advisor Mike Waltz.
King Abdullah is a key US ally but last week rejected "any attempts" to take control of the Palestinian territories and displace its people after Trump stunned the world with his proposal for Gaza.
Half of Jordan's population of 11 million is of Palestinian origin, and since the establishment of Israel in 1948, many Palestinians have sought refuge there.
In 1970 in what became known as "Black September," clashes erupted between the Jordanian army and Palestinian groups led by the Palestinian Liberation Organization (PLO).
It resulted in the expulsion of those groups.
However, Jordan is also keenly aware of the economic pressure that Trump could exercise. Jordan receives around $750 million in economic assistance from Washington annually and another $350 million in military aid.
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