President Biden warned Prime Minister Benjamin Netanyahu of Israel on Sunday that a ground offensive in southern Gaza should not proceed without a plan to protect the more than 1.4 million Palestinians clustered there, the latest sign of frustration by the White House over rising civilian deaths from Israel’s military assault.

During the call on Sunday, according to a description from the White House, the two leaders also discussed ongoing negotiations with Hamas to release Israeli hostages in Gaza in exchange for a cease-fire and the release of Palestinians being held in Israeli jails.

Last week, Mr. Netanyahu bluntly rejected as “ludicrous” a response from Hamas in the negotiations that called for Israel’s withdrawal from Gaza and the freeing of Palestinian prisoners in exchange for the release of more than 100 Israeli hostages in Gaza.

But both American and Israeli officials have said subsequently that there is still room for compromise in the negotiations. A senior administration official who spoke about Mr. Biden and Mr. Netanyahu’s call on the condition of anonymity expressed optimism about the state of the talks, adding that they would continue over the next week to address “significant gaps” between the two sides.

“The president emphasized the need to capitalize on progress made in the negotiations to secure the release of all hostages as soon as possible,” according to the White House statement. “He also called for urgent and specific steps to increase the throughput and consistency of humanitarian assistance to innocent Palestinian civilians.”

Mr. Biden has strongly supported Israel’s decision to retaliate for the Oct. 7 terrorist attack by Hamas that killed an estimated 1,200 people. But as the White House faces rising pressure from the progressive wing of the Democratic Party over the administration’s support of Israel’s military, Mr. Biden’s criticism has grown increasingly blunt. On Thursday, he said Israel’s military operations in Gaza were “over the top.”

The comments were another indication of increasing frustration in the White House with Mr. Netanyahu over the soaring number of civilian deaths in Gaza, where more than 27,000 people have been killed, according to health authorities in the strip run by Hamas. Mr. Netanyahu, who is focused on appealing to the far-right flank of his coalition to maintain his hold on power, has also rejected the Biden administration’s call for a two-state solution after the war.

The White House has said on multiple occasions in recent days that it does not support Mr. Netanyahu’s likely invasion of Rafah, which sits on the border with Egypt. More than half of Gaza’s 2.2 million people are now sheltering in the city, many of them displaced after the Israeli military told them to flee south to avoid the war in the north.

Mr. Biden on Sunday “reaffirmed his view that a military operation in Rafah should not proceed without a credible and executable plan for ensuring the safety of and support for the more than one million people sheltering there,” according to the White House.

In an interview with ABC News that aired on Sunday, Mr. Netanyahu said, without giving specifics, that Israel was “working out a detailed plan” to move Gazans north of Rafah. Egypt has already said it will not accept Palestinians who try to cross the border.

Mr. Biden is expected to discuss the war again on Monday when he hosts King Abdullah II of Jordan at the White House.