Some Israelis want the government to agree to a deal that would free the remaining hostages in exchange for an end to the Israeli assault, fearing that the offensive puts them in jeopardy. Mr. Netanyahu said in a statement on Monday that “only continued military pressure, until total victory, will bring about the release of all of our hostages.”

Mr. Netanyahu says that securing Rafah is critical to Israel’s goal of ending Hamas control in Gaza. On Sunday, he promised civilians there safe passage to areas of northern Gaza, though he offered no details.

President Biden, after meeting at the White House on Monday with King Abdullah II of Jordan, reiterated American concerns about an Israeli invasion in Rafah, saying it “should not proceed” without “a credible plan for ensuring the safety and support of more than one million people sheltering there.”

Calling civilians there “exposed and vulnerable,” Mr. Biden said, “They need to be protected.”

He said that the United States was also continuing to work on a deal between Hamas and Israel that would free the remaining hostages and pause the fighting for at least six weeks.

King Abdullah said the war must end.

“We cannot afford an Israeli attack on Rafah,” he said. “It is certain to produce another humanitarian catastrophe.”

At a news conference in Washington on Monday, Matthew Miller, a State Department spokesman, said the Biden administration had communicated its concerns about the expected invasion to Mr. Netanyahu and other Israeli officials.

But Mr. Miller declined to say what action the United States might take if Israel did not heed its advice. When asked if the Biden administration was happy with the results so far of its efforts to influence Israel’s conduct of the war, he said, “in many cases, no, absolutely we are not.”

More than 28,000 people in Gaza have been killed in Israel’s military campaign, according to the territory’s health officials. Israel says that about 1,200 people were killed in the Oct. 7 attack.

The United Nations has repeatedly warned that an advance on Rafah could be devastating to civilians and could worsen the humanitarian catastrophe already unfolding in Gaza, where people are running dangerously low on food, clean water and medicine.

On Monday, Stéphane Dujarric, a spokesman for the United Nations secretary-general, suggested that the U.N. would play no part in Israel’s evacuations plans. “We will not be party to forced displacement of people,” Mr. Dujarric said. “As it is, there is no place that is currently safe in Gaza.”

Reporting was contributed by Michael Levenson, Iyad Abuheweila, Abu Bakr Bashir, Yan Zhuang, Gabby Sobelman, Mike Ives, Matthew Mpoke Bigg, Farnaz Fassihi, Andrés R. Martínez and Isabel Kershner.