A Navy warship off the coast of Yemen fired missiles at Houthi rebel targets on Thursday. The rebels, engaged in a civil war with the Yemeni government, had reportedly fired on another American ship days earlier.  By U.S. NAVY on October 13, 2016. Photo by Blake Midnight/U.S. Navy. Watch in Times Video »

WASHINGTON — For the United States, it was simple retaliation: Rebels in Yemen had fired missiles at an American warship twice in four days, and so the United States hit back, destroying rebel radar facilities with missiles.

But for the rebels and many others in Yemen, the predawn strikes on Thursday were just the first public evidence of what they have long believed: that the United States has been waging an extended campaign in the country, the hidden hand behind Saudi Arabia’s punishing air war.

For the Obama administration, the missile strikes also highlighted the risks of a balancing strategy it has tried to pursue in Yemen since a bitter sectarian war engulfed the country two years ago. The United States has not formally joined the Saudi-led coalition that intervened in support of Yemen’s deposed government — and has tried to push the warring factions toward a peace deal — but it has refueled coalition bombers, trained Saudi pilots and provided intelligence to the bombing campaign.

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A year and a half of bombing — along with the deaths of thousands of Yemeni civilians — has stoked anger in Yemen not only toward the Saudis, but also toward their perceived patrons in Washington. This week’s attacks on the Mason, an American destroyer, and the Pentagon’s response show how rapidly the United States can go from being an uneasy supporting player to an active participant in a chaotic civil war.

“The Americans have been patronizing and directing the war from the very beginning,” said Brig. Gen. Sharaf Luqman, a spokesman for the rebel alliance.

Yemen’s conflict started in 2014, when Shiite rebels from the north, the Houthis, seized the capital, Sana, and sent the government into exile. They now control much of the country’s north and west, along with army units loyal to former President Ali Abdullah Saleh. An international military coalition led by Saudi Arabia began a bombing campaign in March 2015 in an effort to restore the government of Abdu Rabbu Mansour Hadi, the exiled president.

The Obama administration gave its immediate support to the campaign — despite skepticism about whether the coalition would be able to dislodge the Houthis from Sana — in part because it needed Saudi support for the nuclear deal it was negotiating with the kingdom’s archenemy, Iran.

That support has come under greater scrutiny amid reports that coalition forces have been striking residential areas, markets, medical facilities and weddings. On Saturday, an attack on a funeral reception in Sana killed more than 100 people.

The United States has also kept warships in the region to guard a sea lane through which four million barrels of oil pass each day. There, in the narrow strait at the mouth of the Red Sea, the dizzying mix of warships, cargo vessels and insurgent forces this week yielded precisely what the Obama administration had spent 18 months trying to avoid.

The American strikes, launched at rebel-held territory, came after two unsuccessful missile attacks on the Mason in four days, the Pentagon said Thursday, and were intended solely to protect American forces and other shipping in Bab el Mandeb, the strait separating Yemen from Eritrea and Djibouti.

More attacks would invite further retaliation, Peter Cook, the Pentagon spokesman, saidThursday. American and allied warships will continue to patrol the strait, he said, but “we don’t seek a wider role in the conflict.”

That may be the case, but the United States now finds itself facing a dangerous situation in a narrow stretch of water where even small incidents run the risk of inciting a broader conflict.

After the American strikes, Iran said it was sending two warships to the strait, presumably to support the Houthis, an indigenous Shiite group with loose connections to Iran. Saudi Arabia has portrayed the Houthis as an Iranian proxy force and has said that it needed to intervene in Yemen to protect Saudi national security by preventing the rise of a belligerent militia on its southern border.

Foreign diplomats and analysts say Iran’s ties to the Houthis are murkier, although Iran has provided the group with some military support.

Michael Knights, a fellow at the Washington Institute for Near East Policy who studies Yemen, said most of the arms used by the Houthi-Saleh alliance were “legacy matériel,” meaning that they were in the country before the conflict started. Yemen has for a long time been awash in arms, and much of the rebels’ armory came from the Yemeni Army.

But as the conflict has gone on, there has been more evidence of Iranian military support, he said. Along the Yemen-Saudi border, rebels have begun using anti-tank missiles, shoulder-launched rockets and sniper rifles of the same type used by Iranian-backed militias in Iraq and Lebanon.

Pentagon officials could not say whether it was Houthi rebels themselves who had launched the missiles at the Mason or whether they had been fired by allied military units loyal to Yemen’s former president, Mr. Saleh, who are fighting alongside the insurgents.

But Mr. Cook said Thursday that the main issue was the threat to American forces and that the retaliatory strikes had disabled the radar installations that had targeted the Mason.

“These targets were chosen based on our assessment that they were involved in missile launches in recent days, and they were struck in order to defend our ships and their crews and to protect freedom of navigation through a waterway that is vitally important to international commerce,” Mr. Cook told reporters.

Gerald M. Feierstein, a former ambassador to Yemen who was the State Department’s second-ranking diplomat for the Middle East until May, said the rebels most likely acquired the anti-ship missiles in the past few months, probably from Iran.

“This is a relatively new phenomenon,” Mr. Feierstein said, acknowledging that it was unclear whether the decision to launch them at an American warship had been made by senior Houthi leaders or a rogue commander.

On Oct. 1, the Houthis claimed a successful attack on a vessel being used by the United Arab Emirates. While that strike — and the two attacks on the Mason this week — killed no one, they raised the specter that the chaos in Yemen would increasingly threaten international navigation.

“That is why these missile strikes are so significant,” said Mr. Knights, the analyst. “It might be the indication that the Houthis have said, ‘You know what, if we get nothing from the West, then we have nothing to lose.’”

According to the United Nations, more than 4,000 civilians have been killed in Yemen since the bombing campaign began. Even though the Obama administration provides extensive support for the military coalition, the administration’s public position is that it is not a party to the conflict, a stance that rings hollow for many Yemenis.

“In Yemen, this is seen as a U.S. bombing campaign,” said Senator Christopher S. Murphy, the Connecticut Democrat and critic of the war who led an effort in the Senate last month to block a $1.15 billion arms deal with Saudi Arabia.

Mr. Murphy said that the White House should use its leverage over the Saudis, and use the threat of dialing back some of this support to try to rein in a campaign that has been widely condemned as reckless.

“The Saudis have to know that they can’t conduct this campaign without U.S. support,” he said.