But Washington, Mr. Harling said, insisted in each case on maintaining the fiction that its favored local player had a viable chance to rebuild an orderly state — whether moderate rebels in Syria, the Shiite-dominated government in Baghdad or the Hadi government in Yemen.

The Western powers “have to pretend the situation is not as bad as it is, so they don’t have to accept failure and take ownership of the situation,” Mr. Harling said. “In many years of working in the region, I have never seen such a distance between statements and fact.”

The Saudi-led military campaign against the Houthis has led to fears of a burgeoning proxy war among the Middle East’s big powers. But it is unclear how, or if, Iran will directly respond to a campaign led by a coalition of Sunni nations against a Shiite militia force. Some Middle East experts caution that the Houthi rebels are hardly puppets of Tehran, and that Iran spent years largely ignoring the group’s struggles in Yemen.

Stephen Seche, a former American ambassador to Yemen, said that the Houthis had rarely defined their struggle in Yemen in sectarian terms and that their ties to Iran had been overstated by Gulf nations.

“The Saudis and the Sunnis have made this a sectarian issue,” he said. “This military campaign is the Sunni world saying to Iran: Get out of our backyard.”

Saudi officials argue that Iran has orchestrated the Houthi military advance so they can exert influence on yet another Middle Eastern capital and destabilize Saudi Arabia’s southern border. Adel al Jubeir, the Saudi ambassador to Washington, told reporters Thursday that there was evidence that Iranian Revolutionary Guard operatives and Hezbollah fighters had embedded with the Houthis. He called the military campaign a way to protect the Yemeni people as well as “a way of protecting our national interests.” But while Saudi officials welcome American support for the Yemen operation, they are keeping a wary eye on the United States’ interactions with Iran elsewhere in the region.

Leslie Campbell, the regional director of Middle East and North Africa programs at the National Democratic Institute, said that it was hard to ignore the notion that the Saudi-led offensive in Yemen was in part a message to the United States as it negotiates a nuclear deal with Iran and finds, to some degree, common cause with Iranian-backed Shiite militias in Iraq.