Israeli Prime Minister Benjamin Netanyahu said Monday an undisclosed date for a ground invasion of the southern Gaza city of Rafah has been set, even as the White House said its negotiators in Cairo had handed Hamas militants a proposal for a cease-fire and hostage-release deal.

"Today, I received a detailed report on the talks in Cairo,” the Israeli leader said in Jerusalem. “We are constantly working to achieve our goals, first and foremost the release of all our hostages and achieving a complete victory over Hamas.

"This victory requires entry into Rafah and the elimination of the terrorist battalions there. It will happen. There is a date," he said.

The U.S. immediately rebuked Netanyahu. A Pentagon spokeswoman said, "We've been very clear that we don't support operations into Rafah."

"We want to see a credible plan for how they would conduct any operations there" given "substantial" humanitarian concerns about more than a million Palestinian civilians sheltering there, said deputy Pentagon press secretary Sabrina Singh. “We have not seen their official plan put forward."

Talks in Cairo over the weekend included U.S. Central Intelligence Agency chief William Burns, along with Israeli, Hamas and Qatar officials. The White House characterized the negotiations as “serious.”

"Where we are now is that a proposal has been presented to Hamas, and we are waiting on Hamas' response," National Security Council spokesman John Kirby told reporters. "Now, it's going to be up to Hamas to come through."

Kirby declined to discuss the specifics of the proposed deal, adding "that would be one of the surest ways to torpedo that."

The back-and-forth of negotiations over a cease-fire and hostage release coupled with the threat of extended warfare came days after U.S. President Joe Biden warned Netanyahu of the possibility of a change in U.S. support for the Israeli war effort.

Biden demanded that Israel immediately allow more humanitarian aid into the beleaguered war zone to assist famished Palestinians and empower its negotiators to reach an immediate cease-fire.

Biden’s demands came after an Israeli airstrike killed seven international aid workers trying to deliver food to Gaza.

Kirby said that on Sunday, "We saw more than 300 [humanitarian aid] trucks enter Gaza, and that's progress. But obviously, we need to see this number increase, and we need to see it sustained to really address the dire humanitarian situation in Gaza."

Israeli officials are also due to visit the White House in coming days to hear U.S. concerns over the possible Israeli offensive on Rafah.

"We don't support a major ground operation in Rafah," Kirby said. “We also don't see any sign that such a major ground operation is imminent, or that these troops [moved out of Khan Younis] are being repositioned for that kind of a ground operation."

On the war front, Israel’s military said Monday it carried out an airstrike in southern Lebanon that killed a Hezbollah commander who had conducted multiple attacks targeting northern Israel.

An Israeli military statement identified the commander as Ali Ahmad Hassin of Hezbollah’s Radwan Force.

The militant group announced the death of one of its fighters by the same name without giving details about his death.

Israel Defense Forces said the strike also killed two other people.

Cross-border attacks by Israeli forces and Hezbollah militants have been common throughout Israel’s six-month war against Hezbollah ally Hamas.

Also on Monday, the Israeli military said it carried out an airstrike in the Khan Younis area of southern Gaza in response to multiple rocket launches.

Israeli officials announced Sunday the withdrawal of troops from Khan Younis.

Israeli Defense Minister Yoav Gallant said forces were “exiting and preparing for their next missions,” which included an attack on Rafah.

The war has driven more than half of Gaza’s population to Rafah, an area located along the Gaza-Egypt border.

The United States, the United Nations and others have warned of the potential for a humanitarian catastrophe if Israel carries out a major offensive in Rafah.

Israeli officials have pledged to protect the civilians sheltering in the area but have yet to give a detailed plan of where those civilians might safely go.

Netanyahu on Sunday marked six months since the war began and said Israel is close to achieving its goal of eliminating the Hamas terror group.

"We are one step away from victory,” he told his Cabinet. “But the price we paid is painful and heartbreaking."

Even as stalled cease-fire negotiations resumed in Cairo, Netanyahu pledged, "There will be no cease-fire without the return of hostages. It just won't happen."

Hamas is believed to still be holding about 100 hostages in Gaza tunnels, among the 250 or so it captured in its shock October 7 attack on Israel that killed 1,200 people.

As of mid-February, 112 hostages had been freed, most during a weeklong cease-fire in November, while 36 more are believed to have died or been killed in Gaza during the six months of fighting.

Gaza’s Hamas-run Health Ministry says Israel’s counteroffensive has killed more than 33,000 people, two-thirds of them women and children. The Israeli military says the total includes thousands of militants it has killed.

Some information for this report came from Reuters, The Associated Press and Agence France-Presse.