RADA CITY, Yemen — When Houthi fighters swept into this town and broke the grip of Al Qaeda, they were greeted by grateful residents, relieved that a months-long ordeal of bombings and assassinations by the militants might be coming to an end.

That was in October. And for a time, the Houthis were able to bring “security and stability” to Rada, said Abdullah Idris, a resident who said he had lost a relative in a Qaeda suicide bombing. He was doubtful it would last. “Al Qaeda regrets leaving Rada,” he said. “They will take their revenge.”

A few days after Mr. Idris spoke last month, militants sent two car bombs to attack a Houthi checkpoint, the explosions shredding a passing school bus and killing 16 girls, part of a nationwide outburst of violence.

After Houthi fighters seized control of the Yemeni capital of Sana in September, promising radical political reforms, their supporters were hopeful that they could restore a stability that has eluded Yemen since the uprising against the country’s longtime ruler, Ali Abdullah Saleh, in 2011. Houthi fighters fanned out across the country to assert their control.