President Biden and his aides viewed Israel’s strike on Iran on Friday as a relatively measured response to the barrage of missiles and drones Tehran launched toward Israel last weekend, and they are increasingly hopeful that the confrontation between the two states will not immediately spark a regional escalation, according to several people familiar with the White House’s thinking, speaking on the condition of anonymity to describe internal assessments.

The Biden administration had publicly urged Israel not to respond to the more than 300 missiles and drones Iran launched toward Israeli territory last weekend, about two weeks after an Israeli strike on an Iranian consulate in Syria killed a top general and several others.

Israel’s strike was in a sense a rejection of Biden’s request, but senior officials have concluded that Israel’s decision to aim at a remote part of Iran that did not appear to harm anyone — followed by a muted reaction by Iranian state media — makes it less likely that the tit-for-tat strikes will escalate into a broader war. An Israeli official, who spoke on the condition of anonymity to discuss sensitive military matters, said the strike was intended mostly to signal to Iran that Israel has the ability to hit targets inside the country.

The White House declined to comment on the strike Friday. Secretary of State Antony Blinken said he would not discuss whether Washington was warned about the strike, but he sought to distance the United States from Israel’s action, saying that “the United States has not been involved in any offensive operations.”

The developments came as a welcome change after six months in which it often seemed to White House officials that Israeli Prime Minister Benjamin Netanyahu took every opportunity to publicly rebuff any demand Biden made. Netanyahu’s defiance came despite unwavering U.S. military and diplomatic support for Israel’s military campaign in Gaza, which has isolated the country on the world stage.

On Sunday, the day after Iran’s retaliatory barrage of missiles and drones, White House officials were deeply worried about how Netanyahu might respond, according to a person familiar with the discussions, who spoke on the condition of anonymity to discuss private conversations. But as the week unfolded and Biden officials had a better sense of the planned Israeli response, they became increasingly optimistic that the United States had been able to mitigate the escalatory risks, a senior official said.

Still, deep disagreements remain between the United States and Israel that have yet to be resolved. Most immediately, U.S. and Israeli officials are preparing to hold another high-level meeting about an impending Israeli operation in the southern Gaza city of Rafah, where some 1.5 million Palestinians are sheltering after fleeing there under Israeli orders.

U.S. officials have made it clear that they oppose a major military operation in Rafah without a “credible” plan to protect the Palestinian civilians there — a task that some officials and experts have said is all but impossible. Israeli officials have said they still plan to go into the city to dismantle the remaining Hamas battalions there.

Even as Biden and his top aides say U.S. support for Israel is “ironclad” in the face of the Iranian threat, they remain firmly opposed to a Rafah operation that does not protect civilians, two people familiar with the discussions said.

And even if a wider conflict does not immediately erupt, Middle East experts and analysts cautioned that the decades-long shadow war between Iran and Israel has now crossed an unprecedented threshold. The two countries have shown that they are willing to strike inside each other’s territories, however carefully — a move both long avoided for fear of sparking a war that could become catastrophic.

“We have not seen the conventional regional war that everyone fears, but at a moment’s notice, anything could go wrong,” said Brian Katulis, vice president of policy at the Middle East Institute. “It’s not a sustainable situation when you look at the whole theater.”

While Israel and Iran have been in a “shadow conflict” for decades, Katulis said, their hostility has now become “an open, low-grade direct military confrontation, and with that comes all sorts of risks.”

Biden and his top aides expended significant energy this week to show Netanyahu that Iran would suffer nonmilitary consequences for its attack so Israel did not need to strike back, according to a senior administration official, who spoke on the condition of anonymity to discuss internal deliberations.

Those efforts included organizing the Group of Seven nations to issue a statement condemning Iran, as well as the United States imposing sanctions on Tehran. U.S. officials hoped that would persuade Israel that Iran was even more diplomatically isolated.

Biden and his aides also tried to reassure Israelis that their ability — along with that of the United States and other partners — to strike down the vast majority of Iran’s drones and missiles had reestablished deterrence, signaling to its neighbors that an attack on Israel would probably be fruitless. Several U.S. officials noted that Israeli leaders have feared looking weak since Oct. 7, when Hamas militants rampaged through the Israel-Gaza border fence and killed 1,200 people, many of them civilians, and took about 250 others hostage.

Israel responded with a punishing military campaign in Gaza that has killed more than 33,000 Palestinians, according to the Gaza Health Ministry, which does not distinguish between civilians and combatants but says the majority of the dead are women and children. Israel’s siege of the enclave has created a humanitarian catastrophe as the health system has collapsed and more than 2 million Palestinians face famine.

But the war has spread beyond Gaza, and U.S. officials have long feared that it would escalate into a major regional conflagration that would further destabilize the Middle East. Israel is also fighting Hezbollah in Lebanon on its northern border, where rocket fire has killed and injured people on both sides of the border. Tens of thousands of Israelis have yet to return to their homes in the north because of the fighting.

The escalation with Iran has especially raised fears of how Hezbollah might react if tensions continue to rise. Hezbollah is Tehran’s primary proxy group in the region and it has military capabilities far beyond those of Hamas.

“If the Iranians really wanted to pressure Israel intensely, in addition to firing from Iran, they could have had Hezbollah open up across the entire border,” said Bruce Riedel, a senior fellow at the Brookings Institution who worked on Middle East issues in the Clinton administration.