WASHINGTON—As Israel prepares a retaliatory strike against Iran, the Biden administration increasingly resembles a spectator, with limited insight into what its closest Middle East ally is planning—and lessened influence over its decisions.

White House officials say they have been coordinating closely with their Israeli counterparts and are hopeful Prime Minister Benjamin Netanyahu will limit a likely attack against Iran in response to a barrage of missiles Tehran fired at Israel on Tuesday.

Israel’s air defenses were able to parry the Iranian attack, which caused only minor damage to one of its air bases. Israeli officials have conveyed that they don’t feel the need to retaliate immediately or in a massive way, according to White House officials.

U.S. and Israeli officials have been discussing potential targets, including Iran’s oil facilities. President Biden said on Wednesday that he opposed any strikes on Tehran’s nuclear facilities, but on Thursday left open the possibility that he would support an Israeli attack on the oil infrastructure, remarks that sent oil markets surging .

But Israel has not yet made a final decision about what its response will look like—and the White House has been blindsided repeatedly by Israel’s decisions in recent weeks.

Netanyahu ordered the airstrike that killed Hezbollah leader Hassan Nasrallah from a New York hotel room, even as Biden administration officials scrambled at the United Nations a few blocks away to avert a widening Middle East war last week.

The decision to approve the Sept. 27 strike from U.S. soil without alerting the White House beforehand—and later to make public a photo of himself issuing the order—underscored the growing divergence between Netanyahu’s government and the White House.

In the short term, Israel’s unilateral decision-making about striking Iran risks embroiling the Biden administration in another unpopular regional conflict. In the longer term, it could be another flashpoint for critics who say the U.S. gives Israel too much leeway, not using its leverage to rein in its ally.

Earlier in September, White House envoy Amos Hochstein met with Israeli officials in the Israeli military’s Tel Aviv bunker to urge them not to launch a large-scale operation against Hezbollah in Lebanon. He implored them to give efforts to broker an agreement that would push Hezbollah back from Israel’s northern border a chance.

Hours after Hochstein’s meeting with Netanyahu, hundreds of pagers used by Hezbollah militants exploded across Lebanon in an unprecedented attack that killed dozens of people, including children, and wounded thousands more. The following day, bombs in walkie-talkies set off a second wave of explosions .

A barrage of Israeli airstrikes followed, killing more than 500 people in the deadliest day in Lebanon in nearly two decades .

U.S. officials said they didn’t have advanced knowledge of the pager operation, and tried to distance themselves from the attack. It escalated the limited border strikes that Israel and Hezbollah have been waging for almost a year to a more perilous level.

With the presidential election just over a month away, Biden and his team frequently find themselves looking like bystanders, unwilling or unable to rein in an ally they continue to back politically and provide with critical military support.

Since the start of the Gaza war nearly a year ago, Biden has repeatedly called the U.S.-Israel bond unbreakable. But his nearly 50-year relationship with Netanyahu has steadily deteriorated, cleaved by their clashing political agendas and conflicting war aims. Biden hasn’t spoken to Netanyahu since Aug. 21.

“Biden and Netanyahu have taken each other’s measure, and Netanyahu seems to consistently judge that he has more space than Biden thinks he does,” said Jon Alterman , director of Middle East programs at the Center for Strategic and International Studies. The U.S. “seems to be treated by the Israeli leadership as either a nag or a back-seat driver who doesn’t understand the requirements at the moment.”

U.S. attempts to rein in Israel in Gaza yielded only limited results, analysts say. In Lebanon, Netanyahu has appeared even less constrained. White House officials aren’t unhappy at the blows Israel has delivered to Hezbollah, a U.S.-designated terror group. Nor are they eager a month before the U.S. presidential election to be seen as reining in an attack on Tehran.

For almost a year, senior Biden officials have shuttled across the region to prevent Israel’s war against Hamas from spiraling into a broader conflict. U.S. officials cited incremental progress—an agreement to allow some humanitarian assistance into Gaza, the withdrawal of some Israeli troops from the strip—as evidence that the Israelis were willing to listen to its warnings about the danger of a regional war.

But as Israel seized the chance to dismantle Hezbollah in an attempt to end the group’s attacks on its northern border and allow tens of thousands of displaced Israelis to return home, Netanyahu has repeatedly disregarded U.S. calls for restraint.

Driving the shift in the U.S.-Israel relationship is the transformation in Israel, traumatized by the Hamas terrorist attack and led by a prime minister bent on shoring up his support among Israelis who favor aggressive military moves to deliver lasting defeats to adversaries.

“Oct. 7 changed everything,” says David Schenker, who served as assistant secretary of state for Near Eastern affairs during the Trump administration. “We are dealing with a new Israel that is going to relentlessly pursue its security objectives with less regard for U.S. sensitivities.”

At the same time, the political landscape in the U.S. has also changed. Netanyahu, a keen observer of U.S. politics, knows that Biden officials are hamstrung by the coming presidential election.

“You’re not going to find an American negotiator, weeks before one of the most consequential elections in modern American history, pushing and pressing the Israelis, particularly on a front that involves Iran,” says Aaron David Miller, a former State Department Middle East official.

U.S. officials have worked for months to head off an escalation of the Israel-Hezbollah fighting in Lebanon, fearing it could draw in Iran and force the U.S. to become more deeply involved militarily.

As Israeli airstrikes pounded Lebanon last month, American and French diplomats in New York for the annual U.N. General Assembly raced to find a way to stop the violence.

Israeli officials backed a statement from the U.S., France and other countries calling for a 21-day cease-fire to allow negotiations between Israel and Hezbollah, according to U.S. officials. But Netanyahu backed out of the U.S.-brokered cease-fire plan after the opportunity arose to target Nasrallah, with his office declaring in a Sept. 26 statement that he had directed Israeli forces to “continue fighting with full force.”

Israel had been “fully informed and fully aware of every word” in the cease-fire proposal, an exasperated White House spokesman told reporters. After the airstrike that killed Nasrallah on Friday in Beirut, U.S. officials said Israel had only informed them of the imminent attack when the planes were in the air.

Top Biden officials quickly adjusted, saying afterward that they welcomed Nasrallah’s death. As Israel began preparing to send ground troops across the Lebanese border, the administration said it was confident that the incursion would be limited.

“I’m comfortable with them stopping,” Biden said when asked Monday if he was aware that Israel looked set to launch a limited ground invasion into Lebanon.

Hours later, Israeli armored tanks rolled across Lebanon’s southern border, as the Israel Defense Forces began what it called “limited” and “localized” raids to dislodge positions held by Hezbollah militants. On Thursday, Israeli forces were pressing deeper into Lebanon.

Write to Lara Seligman at lara.seligman@wsj.com and Vera Bergengruen at vera.bergengruen@wsj.com