The regional war that no one wanted is here. How wide will it be?

Since the outbreak of war between Israel and Hamas nearly 100 days ago, President Biden and his aides have struggled to keep the war under control, fearing that a regional escalation could quickly draw in American troops.

Now, with the American-led strike in nearly 30 locations in Yemen on Thursday and a smaller strike the next day, it is no longer a question of whether a regional conflict will emerge. It has already started. The biggest questions now are the intensity of the conflict and whether it can be contained.

This is exactly the outcome that no one wanted, probably not even Iran.

“We are not interested in a war with Yemen. We are not interested in any conflict,” White House spokesman John F. Kirby said Friday. “In fact, everything the president has done has tried to prevent any escalation of the conflict, including last night's strikes.”

Biden's decision to launch airstrikes after resisting calls to act against Yemen-based Houthi militants whose repeated attacks on Red Sea shipping have begun to take their toll on global trade a clear change in strategy. After issuing a series of warnings, officials said, Mr. Biden felt his hand was forced after a barrage of missile and drone attacks on Tuesday targeted a U.S. cargo ship and the Navy ships surrounding it.

“This is already a regional war, no longer limited to Gaza but spreading to Lebanon, Iraq, Syria and Yemen,” said Hugh Lovatt, a Middle East expert for the European Council on Foreign Relations. Washington, he added, wanted to demonstrate its willingness to deter Iranian provocations, so it conspicuously positioned its aircraft carriers and fighter jets to respond quickly. But those same views leave the United States more vulnerable.

Over the course of twelve weeks, attacks on Israeli, American, and Western interests have come from Lebanon, Iraq, and Syria, prompting modest, carefully targeted responses from U.S. and Israeli forces. The United States has also issued warnings to Iran, which the Americans say is acting as a loose coordinator.

What was striking about the retaliatory attack in Yemen was its scale: Using fighter jets and sea-launched missiles, US and British forces, supported by a small number of other allies, hit a large number of Houthi missiles and drone sites.

Mr. Biden is walking a fine line between deterrence and escalation, and his aides admit there is no science behind the calculation. Tehran and its allies, including Hezbollah in Lebanon, have been cautious in their support of Hamas and have kept their actions contained, to avoid a larger US military response that could undermine Tehran's exercise of power in Lebanon, Iraq and Syria to threaten.

But how much control Iran has over its allies is up for debate, and its leaders could also be misinterpreting the American and Israeli red lines.

The Houthis, a small Iranian-backed tribe in Yemen, are among the most aggressive in pushing borders, trying to block international trade routes through the Red Sea and ignoring American and Western warnings to stop doing so.

Houthi officials say the sole purpose of their attacks is to force Israel to halt its military campaign and allow the free flow of aid into Gaza.

Western diplomats said there was reluctance to strike back against the Houthis, partly to avoid disrupting the ceasefire in Yemen's civil war, and partly because of the difficulty of completely eliminating their threat. But the Houthis' repeated attacks on ships, their direct fire on U.S. helicopters and their attack Tuesday on a U.S. cargo ship left the United States with what officials say was no real choice.

US officials said the Pentagon launched a second round of strikes against the Houthis on Friday, bombing a radar facility in Yemen.

It is not known how long it will take before the Houthis will recover and threaten the ships in the Red Sea again, as they have promised. So far, the response has been muted, with only a single anti-ship missile fired harmlessly into the Red Sea, far from any passing ship, a Pentagon official told reporters earlier on Friday.

But deeper U.S. military involvement also contributes to the perception in the larger world that the United States is acting even more directly on Israel's behalf, risking further damage to U.S. and Western standing as the death toll in Gaza rises. Israel is now defending its conduct against charges of genocide before an international court.

Iran is using allies like Hezbollah and the Houthis to distance itself from their actions and maintain its credibility in the region, trying to avoid a direct attack that could jeopardize the Islamic Revolution and its nuclear program.

But Iran is also being pulled along by those same proxies.

“Iran is really pushing for it,” said François Heisbourg, a French military analyst. “It's another reason why they don't want war now: they want their centrifuges to run peacefully.” The Iranians do not have a nuclear weapon, but could enrich enough uranium to weapons grade within a few weeks, from the current 60 percent enrichment to 90 percent, he said. “They did 95 percent of the work.”

Israel is also increasing its attacks on Iranian allies, especially in Lebanon and Syria. Following the attack by Hamas, Hezbollah in Lebanon began a series of attacks from Lebanon, prompting Israel to evacuate civilians near the conflict.

After that, Israel's air campaign killed 19 Hezbollah members in Syria in three months, more than twice as many in the rest of 2023 combined, according to a Reuters tally. During the same period, more than 130 Hezbollah fighters were also killed by Israel in Lebanon.

Amine Hoteit, a retired Lebanese army general and analyst, listed several objectives of the Israeli strikes in Syria: to maintain attention there and to pressure the Syrian government “to cut off the Iranian supply route.”

U.S. troops deployed in Iraq and Syria to prevent an ISIS resurgence have been attacked by Iran-backed militias 130 times since Oct. 17, according to the Pentagon's count Thursday, with a total of 53 attacks in Iraq and 77 in Syria. The United States has retaliated less than a dozen times, mostly after American casualties.

Each time, the United States has said its response is intended to deter further attacks and is aimed at sending a message to Iran and its allies, who operate freely in Iraq and Syria. But no American troops were killed. The concern, according to U.S. officials, is that sooner or later one of the strikes will kill troops, and the response would then be much deadlier and could spiral out of control.

On January 4, the US military launched a rare retaliatory strike in Baghdad, killing a militia leader it blames for recent attacks on US personnel, a move condemned by the Iraqi government.

Although the Iraqi government is now dominated by parties close to Iran, the American presence is largely tolerated due to fears that the Islamic State could quickly regain ground without American help.

But on Friday, the Iraqi Foreign Ministry condemned the attacks on the Houthis in Yemen. “We believe that expanding the scope of the targets does not represent a solution to the problem – rather it will lead to an expansion of the scope of the war,” the statement said.

While the main focus has been on Hamas in Gaza and Hezbollah, the Houthi threat to trade has the potential for the greatest global impact, as about 30 percent of the world's container ships pass through the Red Sea. Volvo, Tesla and other automakers in Europe have already suspended production for a few days or more due to disruptions in receiving parts as ships sail around the Red Sea and Suez Canal.

The United States and more than a dozen other countries have formed a coalition to protect shipping, Operation Prosperity Guardian. But the Houthis have continued to try to attack ships, with or without Israeli connections, and Maersk decided to suspend all shipping in the Red Sea after a December 31 attack on one of his ships. It has warned its customers to expect significant disruptions, and analysts expect higher prices will contribute to global inflation.

In public speeches this week, Iran's Supreme Leader Ayatollah Ali Khamenei and Hezbollah leader Sheikh Hassan Nasrallah reiterated that they do not want extended war. But Colin P. Clarke, a counterterrorism expert and research director at the Soufan Group, said Israel could not afford to be complacent, given the serious miscalculation before October 7 that Hamas was also not interested in war.

Recent killings that have struck at the heart of Iran's ties with Hezbollah and Hamas have unnerved Iranians, who have described them in chat rooms and on social media as “beaten again and again.”

Brig. General Sayyed Razi Mousavi, who was killed in Damascus on Christmas, was responsible for purchasing missiles, rockets and drones for Hezbollah in Lebanon and allied militias in Syria and Iraq for 20 years, according to Iranian media. Mr. Khamenei performed the Prayer of the Dead over his body at his funeral, an honor reserved for the most respected subordinates.

Saleh al-Arouri, deputy political head of Hamas, killed in a drone strike in the heart of Hezbollah's power base in the Dahieh district of Beirut, was the Hamas member closest to Iran and Hezbollah and the person who they most trusted with sensitive messages and facilitating financing and technical know-how from Iran.

Alissa J. Rubin contributed reporting from Baghdad, Hwaida Saad from Beirut, and Helene Kuiper And Erik Schmitt from Washington.