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.