King Abdullah and President Biden have met at the White House to discuss cease-fire options.

President Biden said on Monday that the major ground offensive that Israel is expected to carry out in the southern Gaza city of Rafah should not proceed without a “credible plan” to ensure the safety of more than 1 million people sheltering there.

Mr. Biden spoke after meeting on Monday afternoon with King Abdullah II of Jordan, a key figure in the push for a cease-fire in the Gaza Strip, in the first face-to-face conversation between the two leaders since the Israel-Hamas war started.

The president said he and the Jordanian monarch discussed the cease-fire talks, with Mr. Biden suggesting a six-week pause in the fighting that could allow for the release of hostages held by Hamas and the forging of something “more enduring.”

Mr. Biden said he was particularly concerned about the situation in Rafah, where Israeli forces conducted a rare rescue mission early on Monday to free two men held hostage for more than four months, and displaced Gazans fear an invasion that will leave them nowhere to flee.

“Many people there have been displaced, displaced multiple times fleeing the violence to the north,” Mr. Biden said. “And now they’re packed into Rafah, exposed and vulnerable. They need to be protected.”

The visit came as the king sought to shore up international support for an immediate cease-fire in Gaza — which Mr. Biden has repeatedly rejected — and as the U.S. continued to apply pressure on Israel to mitigate casualties and civilian displacements.

King Abdullah said an Israeli invasion of Rafah was “certain to produce another humanitarian catastrophe.”

“The situation is already unbearable for over a million people who had been pushed into Rafah since the war started,” he said. “We cannot stand by and let this continue. We need a lasting cease-fire now. This war must end.”

Ahead of the meeting, John F. Kirby, a White House spokesman, said that the U.S. continued to reject the idea of a general cease-fire that would permanently halt the fighting, but that President Biden also still supported a humanitarian pause.

“We want to see the war end as soon as possible,” he said. “And we believe one of the first steps that’s critical to doing that is a humanitarian pause, an extended pause longer than what we saw back in November of a week, that would allow us to get all the hostages out, get more aid and assistance in, and then hopefully lead to discussions that can get us closer to an end to the conflict.”

Egypt and Qatar, acting as intermediaries between Israel and Hamas, have led talks aimed at halting the fighting and freeing hostages held in Gaza. The Biden administration has been actively involved in those negotiations, working publicly and behind the scenes to try to advance a cease-fire deal.

The C.I.A. director, William J. Burns, was expected to travel to Cairo for continued talks on Tuesday on the hostages, according to a U.S. official who spoke on condition of anonymity about the talks. Mr. Burns’s planned trip was disclosed by a U.S. official, who spoke on condition of anonymity because of the sensitivity of the discussions.

While Prime Minister Benjamin Netanyahu of Israel last week publicly dismissed a Hamas proposal, Israeli officials have signaled that their government is still open to negotiation. The mere fact that more talks will be taking place in Cairo this week is seen as a positive sign.

Ahead of the meeting between Mr. Biden and King Abdullah, the White House said they would speak about “efforts to produce an enduring end to the crisis” in Gaza, where health officials say more than 28,000 people have been killed since the start of the war.

Much of Jordan’s population is ethnically Palestinian, putting the country — a close U.S. ally that has a peace treaty with Israel — in a tricky position as it navigates the fallout from the war.

King Abdullah has repeatedly called for an immediate cease-fire and for the delivery of more humanitarian aid into Gaza. He led a summit meeting in Jordan last month about the situation in the enclave and has been working in concert with other Arab leaders to push for a halt to the fighting.

Jordan and Israel share a border, in addition to maintaining a crucial regional alliance. The kingdom is the custodian of the Aqsa compound in Jerusalem, a key holy site in Islam that is also revered by Jews, who call it the Temple Mount. The compound has often been a source of disputes between Israelis and Palestinians.

But relations between Jordan and Israel grew tenser in recent years. And since Israel launched a retaliatory war against Hamas in Gaza in response to the deadly Oct. 7 attacks, King Abdullah has repeatedly criticized how Israel has carried out its assault.