While the council pays salaries and distributes fuel, Al Qaeda maintains a police station to settle disputes, residents said. It has so far made no effort to ban smoking or regulate how women dress.

Nor has it called itself Al Qaeda, instead using the name the Sons of Hadhramaut to emphasize its ties to the surrounding province.

One self-described Qaeda member said that the choice of name was deliberate, recalling that after the group seized territory in southern Yemen in 2011, the country’s military had mobilized to push it out with support from the United States.

“We were in control for a year and six months, we applied God’s law, we created a small state and the whole world saw it, but they did not leave us alone,” the man said in an interview with a Yemeni television station. “So we came here with the name the Sons of Hadhramaut, but the people here know who we are.”

American officials have long considered the terrorist group’s Yemeni branch, known as Al Qaeda in the Arabian Peninsula, the most dangerous to the West. It has sought to carry out attacks against the United States, and it retains sophisticated bomb-making expertise.

Now, Yemen’s civil war has given the group an opportunity to expand, analysts said.

After Houthi rebels seized the Yemeni capital and forced the president into exile, Saudi Arabia began leading a bombing campaign aimed at pushing the Houthis back. With all that going on, no one has tried to dislodge Al Qaeda from Al Mukalla, although American drone strikes have killed top Qaeda leaders nearby.

April Longley Alley, a Yemen analyst with the International Crisis Group, said there was reason to worry that the close ties between Qaeda fighters and other armed elements meant that any foreign military support given to fight the Houthis could eventually end up in Al Qaeda’s hands.