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.”