The United States and Britain carried out large-scale military strikes on Saturday against multiple sites in Yemen controlled by Houthi militants, according to a statement from the two countries and six allies, as the Biden administration continued its reprisal campaign in the Middle East targeting Iran-backed militias.

The attacks against 36 Houthi targets at 13 sites in northern Yemen came barely 24 hours after the United States carried out a series of military strikes against Iranian forces and the militias they support at seven sites in Syria and Iraq.

American and British warplanes, as well as Navy Tomahawk cruise missiles, hit deeply buried weapons storage facilities; missile systems and launchers; air defense systems; and radars in Yemen, the statement said. Australia, Bahrain, Denmark, Canada, the Netherlands and New Zealand provided support, which officials said included intelligence and logistics assistance.

“These precision strikes are intended to disrupt and degrade the capabilities that the Houthis use to threaten global trade and the lives of innocent mariners, and are in response to a series of illegal, dangerous and destabilizing Houthi actions since previous coalition strikes,” the statement said, referring to major attacks by the United States and Britain last month.

The attacks were the second-largest salvo since the allies first struck Houthi targets on Jan. 11. They came after a week in which the Houthis had been particularly defiant, launching several attack drones and cruise and ballistic missiles at merchant vessels and U.S. Navy warships in the Red Sea and the Gulf of Aden.

The American-led air and naval strikes began last month in response to dozens of Houthi drone and missile attacks against commercial shipping in the Red Sea since November. The Houthis claim their attacks are in protest of Israel’s military campaign against Hamas in Gaza.

The United States and several allies had repeatedly warned the Houthis of serious consequences if the salvos did not stop. But the U.S.-led strikes have so far failed to deter the Houthis from attacking shipping lanes to and from the Suez Canal that are critical for global trade. Hundreds of ships have been forced to take a lengthy detour around southern Africa, driving up costs.

“Our military operations against the Zionist entity will continue until the aggression against Gaza stops, no matter what sacrifices it demands from us,” a senior Houthi official said in response to the latest attacks. “We will meet escalation with escalation.”

While the Biden administration maintains that it is not looking to widen the war in the region, the strikes over the past two days represent an escalation.

In scope, the strikes in Yemen were roughly the size of U.S. and British attacks on Jan. 22, but smaller than the salvos on Jan. 11, officials said.

The strikes on Saturday came after a back-and-forth exchange of more limited attacks in the previous 36 hours between the Houthis and U.S. forces in the Red Sea and nearby waters.

A protest in Sana, Yemen, on Friday. The Houthi militia in Yemen has vowed to keep up its attacks as long as Israel continues its invasion of Gaza.Credit…Yahya Arhab/EPA, via Shutterstock

At about 10:30 a.m. local time on Friday, the destroyer Carney shot down a drone flying over the Gulf of Aden. Six hours later, the United States attacked four Houthi attack drones that the military’s Central Command said were about to launch and threaten merchant ships in the Red Sea. At about 9:20 p.m., U.S. forces struck cruise missiles in Houthi-controlled areas of Yemen after determining they presented a threat to vessels in the region, Central Command said in another release. And about five hours after that, early Saturday, the destroyer Laboon and FA-18 attack planes shot down seven drones flying over the Red Sea.

Then on Saturday night, before the planned strikes, the United States hit six Houthi anti-ship cruise missiles as they were being prepared to launch against ships in the Red Sea, Central Command said.

So far, the Biden administration has been trying to chip away at the ability of the Houthis to menace merchant ships and military vessels without killing large numbers of Houthi fighters and commanders, which could potentially unleash even more mayhem into a widening war.

“I don’t see how these airstrikes achieve U.S. objectives or avoid further regional escalation,” said Stacey Philbrick Yadav, a Yemen specialist at Hobart and William Smith Colleges. “While they may degrade Houthi capabilities in the short term, the group’s leadership has vowed to continue its Red Sea attacks and to retaliate in response to these airstrikes.”

Saturday’s strikes came as the U.S. military had begun assessing the dozens of airstrikes it conducted Friday night that hit 85 targets at seven sites in Iraq and Syria.

The strikes were in retaliation for a drone attack on a remote outpost in Jordan last Sunday that killed three American soldiers. Washington has suggested that an Iran-linked Iraqi militia, Kataib Hezbollah, was behind that attack.

Syria and Iraq said Friday’s strikes killed at least 39 people — 23 in Syria and 16 in Iraq — a toll that the Iraqi government said included civilians.

The multiple strikes left the region on edge, though analysts said they seemed designed to avoid a confrontation with Iran by focusing on the operational capabilities of the militias.

“We do not seek conflict in the Middle East or anywhere else,” the U.S. defense secretary, Lloyd J. Austin III, said after the Friday strikes, “but the president and I will not tolerate attacks on American forces.”

The reaction from Iranian officials to Friday’s round of strikes was condemnatory but not inflammatory. A Foreign Ministry spokesman, Nasser Kanaani, said the U.S. attacks represented “another strategic mistake,” but did not speak about striking back.

Syria and Iraq denounced the U.S. strikes in their countries as violations of their sovereignty, adding that the attacks would only impede the fight against Islamic State militants.

Washington not only calibrated the attacks to avoid stoking a broader war, but had openly warned that they were coming days in advance of the strikes, said Maha Yahya, the director of the Carnegie Middle East Center in Beirut, Lebanon. Both sides, she added, had sought ways to attack that remained “below a threshold that would spell an all-out war.”

The stakes of this particular American bombing were high, given rising tensions across the Middle East because of the war in Gaza and related violence it has fueled elsewhere in the region.

The rubble of a destroyed building in Al-Qaim, Iraq, on Saturday after a U.S. airstrike the night before.Credit…Reuters

Since the deadly Hamas-led assault on Israel on Oct. 7, and Israel’s retaliatory bombing campaign and ground invasion in Gaza, Iran-backed militias have carried out more than 160 attacks on U.S. forces in the region, as well as on commercial ships in the Red Sea.

The Houthis in Yemen have said they will not stop the attacks in the Red Sea until there is a cease-fire in Gaza. Mr. Kanaani, the Iranian foreign minister, echoed that sentiment, saying on Saturday that the “unlimited support for the U.S.” for Israel was a main driver of regional tensions.

Secretary of State Antony J. Blinken will return to the region this week to continue negotiations on the release of Israeli hostages and a temporary cease-fire. More than 27,000 Palestinian have died in the conflict, according to Gazan health officials, and about 1,200 Israelis have been killed, Israeli officials said. More than 100 hostages kidnapped from Israel in the Oct. 7 assault remain captive in Gaza.

The three U.S. soldiers killed in Jordan were the first to die in Gaza-related military violence since the war began. The United States said it struck only targets associated with militias backed by Iran that had been involved in the attack on the base in Jordan, or in other offensives against U.S. troops.

But the United States did not attack Iran itself, despite its status as the patron and overall coordinator of these militias. Nor did it strike Hezbollah in Lebanon, the most powerful of Iran’s regional proxies, which has been battling Israeli troops along the Lebanon-Israel border throughout the war in Gaza.

That fits with the United States’ efforts to keep its own military activities separate from those of Israel, which says it is seeking to destroy Hamas.

How successful the new strikes will be in degrading the military capabilities of Iran and its proxies — or in deterring them from attacking the United States — remains an open question.

Iran created its network, with affiliates in Lebanon, Syria, Iraq and Yemen, to extend its influence and give it a way to strike foes without having to do so itself, analysts say. Anti-Iran hawks in the United States and the Middle East often argue that attacking the proxies without hitting Iran is a waste of time.

Ms. Yahya of the Carnegie Center said she did not expect the new U.S. strikes to drastically change the activities of Iran’s regional proxies.

“The only thing that will get them to pull back would be a clear sign from Iran telling them to pull back,” she said. “But even then, they may listen and they may not.”

That is because Iran does not directly control its proxies, who have significant latitude to make their own decisions, Ms. Yahya said.

Reporting was contributed by Raja Abdulrahim and Aaron Boxerman from Jerusalem, Max Bearak from New York, Ben Hubbard from Istanbul, Hwaida Saad from Beirut and David E. Sanger from Berlin.