Yemeni Shiite supporters of the Huthi movement chant slogans before dismantling part of their protest camp in Sanaa on October 16, 2014. (Mohammed Huwais/AFP/Getty Images)

PRESIDENT OBAMA cited Yemen as a model for U.S. operations against the Islamic State last month, not long after he told an interviewer that the intervention in Libya was his greatest foreign policy regret. In fact, the two countries offer similar lessons in the deficiencies of Mr. Obama’s strategy. By backing local forces with airpower in Libya, the United States and its allies were able to overthrow a murderous regime — but, as Mr. Obama acknowledged, the failure to assist with building a state afterward has facilitated Libya’s collapse into chaos.

Now Yemen appears in danger of disintegrating, as sectarian insurgents backed by Iran capture large parts of the country’s north, even while al-Qaeda forces surge in the south. Once again a narrowly focused U.S. engagement has helped make the breakdown possible.

The Obama administration has conducted extensive military operations in Yemen, but they have been strictly aimed at carrying out strikes against al-Qaeda operatives believed to be plotting against the United States. U.S. trainers in the country have worked with counterterrorism forces, eschewing an attempt to build a reliable national army. While U.S. diplomats and envoys such as CIA Director John Brennan helped to broker the political transition that removed former dictator Ali Abdullah Saleh after 33 years in office, only minimal resources have gone toward building Yemeni political institutions, such as courts and civil society.

Now the administration is watching as the political and security order it backed unravels. Insurgents known as Houthis, who adhere to an offshoot of Shiite Islamism, first captured the capital, Sanaa, late last month and dictated terms to U.S.-backed president Abed Rabbo Mansour Hadi. Now they have seized a major Red Sea port that contains Yemen’s largest oil refinery and are continuing to advance southward. As government forces crumble or disappear, al-Qaeda is expanding its hold over parts of the south, where an independence movement is also reviving.

A State Department spokesman said Wednesday that the administration is not sure what the Houthis’ objectives are; Yemen-watchers believe they could range from forcing changes in a proposed federalization scheme for the country to creating a new state under the Houthis’ control. But the movement’s hostility toward the United States and its principal allies in the region is not in doubt. U.S. officials believe the Houthis have received materiel and training from Iran; their slogan, including the phrase “death to America,” is taken from the Iranian Revolutionary Guard Corps and Lebanon’s Hezbollah. Saudi Arabia, which joined one of the Yemeni government’s six military campaigns against the Houthis before 2010, sees the movement as a major threat.

The Houthis’ surge may make it impossible for the Obama administration to continue critical operations against al-Qaeda, which reportedly have included 19 drone strikes this year alone. It should force a reexamination of Mr. Obama’s model of managing threats from jihadist movements with narrowly focused training and advising of local forces and no effort to help build national institutions. Interventions that ignore the need to create functioning political systems and professional forces that can ensure domestic security only open the door to failed states — and heightened threats to the United States.