President Biden’s warning over halting weapons supplies has tightened the bind that Prime Minister Benjamin Netanyahu of Israel faces, as he is increasingly caught between international calls for a cease-fire and right-wing Israeli demands to proceed with a wide-scale invasion of Rafah, in southern Gaza.

Mr. Netanyahu, who has insisted over American objections that invading Rafah is necessary, now finds the U.S.-Israel relationship at a moment of crisis that could affect how he conducts the next phase of the war against Hamas.

On Thursday, the Israeli leader, alluding to Mr. Biden’s remarks, said in a statement: “If we need to stand alone, we will stand alone. I have said that, if necessary, we will fight with our fingernails. But we have much more than fingernails and with that same strength of spirit, with God’s help, together we will win.”

With Mr. Biden threatening for the first time to withhold more American weapons, including heavy bombs and artillery shells, if Israel carries out a major operation in Rafah, a city crammed with about a million Palestinians, analysts say that the Israeli military risks losing the support of its most important supplier of foreign arms.

“The United States provides Israel with a steel dome — it’s not only military support; it’s strategic and political; it’s at the United Nations, the international court, and so on,” said Amos Gilead, a former senior Israeli defense official who worked closely with American security officials for decades.

“If we lose the United States with the unbelievable friendship of President Biden, it won’t be forgiven,” he added.

But Rear Adm. Daniel Hagari, spokesman for the Israeli military, said on Thursday that the military had sufficient “munitions for its planned operations, including operations in Rafah.”

While Israel has enough weapons in its stockpiles to conduct a wide-scale invasion of the Gazan city, U.S. restrictions could force the Israeli military to cut back on deploying specific munitions, experts said.

“It’s possible we’ll have to economize the way we use our arms and hit more targets without precision bombs,” said Jacob Nagel, a former national security adviser.

Avi Dadon, a former leader of procurement at Israel’s Defense Ministry, told Kan, the Israeli public broadcaster, that he “could be worried” if American arms were withheld. But outwardly, at least, key members of Mr. Netanyahu’s government said the war effort would not be affected.

“I turn to Israel’s enemies as well as to our best of friends and say: The state of Israel cannot be subdued,” Defense Minister Yoav Gallant said at a memorial ceremony, adding that the country would do “whatever is necessary” to defend its citizens and “to stand up to those who attempt to destroy us.”

Bezalel Smotrich, the far-right finance minister, declared that Israel would achieve “complete victory” despite what he described as Mr. Biden’s “pushback and arms embargo.”

An injured Palestinian child was taken to Al Kuwaiti Hospital in Rafah, in southern Gaza, on Wednesday.Credit…Haitham Imad/EPA, via Shutterstock

American-made weapons, including heavy bombs, have been essential to Israel’s war effort since the country was attacked by Hamas and other militant groups on Oct. 7. But Mr. Biden has been under growing domestic pressure to rein in Israel’s military as the death toll has risen in Gaza. It is now more than 34,000, according to local health authorities.

And in his comments on Wednesday in an interview with CNN, Mr. Biden acknowledged for the first time that U.S. bombs had killed innocent civilians in the conflict.

The American concerns have only grown since the Israeli army sent tanks and troops into the eastern part of Rafah on Monday night, taking over the main border crossing between Gaza and Egypt. Israeli forces have stopped short of entering built-up parts of the city, but Mr. Netanyahu and others have signaled that such an operation is necessary to eliminate Hamas battalions there.

On Tuesday, American officials said Mr. Biden had withheld 1,800 2,000-pound bombs and 1,700 500-pound bombs that he feared could be dropped on Rafah. The administration was reviewing whether to hold back future transfers, including guidance kits that convert so-called dumb bombs into precision-guided munitions, the officials said.

In addition to the bombs, Mr. Biden said the United States would not supply artillery shells if Israel invaded population centers in Rafah.

Gilad Erdan, the Israeli ambassador to the United Nations, described the Biden administration’s decision as “very disappointing” and “frustrating.”

“We have a cruel enemy here,” he said. “Is this the time to put restrictions on Israel’s weapons?”

Nadav Eyal, a prominent columnist for a centrist Israeli newspaper, said Mr. Biden had essentially decided to declare an end to the war. Writing on the social media platform X, he called it “the most serious clash between an American administration and the government of Israel since the first Lebanon war.”

The Israeli ambassador to Washington, Michael Herzog, said on Thursday that Mr. Biden’s decision “sends the wrong message to Hamas and to our enemies in the region.”

“It puts us in a corner,” he said in a public conversation hosted by the Carnegie Endowment for International Peace in Washington. He added, “Nobody presented to me or to us a strategy of defeating Hamas without dealing with Rafah.”

Some analysts, however, downplayed the significance of the crisis, arguing it wasn’t as bad as past fissures between the United States and Israel. The rupture in relations over the Iran nuclear deal in 2015 was “much worse,” said Mr. Nagel.

Amid the tense state of affairs, Israel’s president, Isaac Herzog, thanked the United States for supporting Israel and appeared to lash out at Itamar Ben-Gvir, the national security minister, who had posted on X, “Hamas ♥ Biden.”

“Even when there are disagreements and moments of disappointment between friends and allies, there is a way to clarify the disputes,” Mr. Herzog said.

Myra Noveck, Michael Crowley and Johnatan Reiss contributed reporting.