The American military has small units in Yemen that help to manage a campaign of drone strikes against Al Qaeda, as well as provide training for the Yemeni military.

The former head of security for the Interior Ministry in Baihan District, Col. Mubarak Abdullah, confirmed that the army’s 19th Brigade headquarters had fallen to the militants. He said he did not know how many of the brigade’s 4,000 soldiers had been taken prisoner. Colonel Abdullah resigned recently as security chief but is still working in the security office in the district.

The brigade commander was released after a tribal negotiation, Colonel Abdullah said. Yemeni officials said most of the soldiers were allowed to leave with their personal weapons, while the Qaeda militants kept the heavy equipment and artillery stored at the base.

Security officials in the area said 12 soldiers had been killed in the attack but resistance had been ineffective. “Given the shaky situation in the country, the fighting and defensive spirit is no longer with the people because they know no one will save them,” an official said.

It was unclear if the army brigade had previously been under the direct control of the Houthi militants, whose authority in the south and east of the country is unclear and often disputed.

The Houthis effectively took control of the military and the Defense Ministry when the government collapsed on Jan. 22, with the resignation of the American-allied president, Abdu Rabbu Mansour Hadi, after Houthi forces besieged his home.

Western diplomats here said the Houthi military has been trying to extend its power in the oil-rich east and south of the country, but military units in the provinces have loyalties to a variety of power brokers, including Mr. Hadi; his predecessor, Ali Abdullah Saleh, who was ousted as a result of the Arab Spring uprisings in 2011 but remains a political power; and southern political factions.