MANAMA, Bahrain — The United States has tripled the number of airstrikes this year against Al Qaeda’s branch in Yemen, one of the deadliest and most sophisticated terrorist organizations in the world. American allies have pushed the militants from their lucrative coastal strongholds. And the Pentagon recently boasted of killing key Qaeda leaders and disrupting the group’s operations.

Yet the top United States counterterrorism official and other American intelligence analysts concede the campaign has barely dented the terrorist group’s ability to strike United States interests.

“It doesn’t feel yet that we’re ahead of the problem in Yemen,” Nicholas J. Rasmussen, who stepped down this month after three years as the director of the National Counterterrorism Center, said in an interview. “It continues to be one of the most frustrating theaters in our counterterrorism work right now.”

Even as President Trump lauds the demise of the Islamic State’s self-proclaimed caliphate in Iraq and Syria, the threat of a terrorist attack — with the most commonly feared target a commercial airliner — emanating from the chaotic, ungoverned spaces of Yemen remains high on the government’s list of terrorism concerns. The group formally known as Al Qaeda in the Arabian Peninsula, or A.Q.A.P., has dogged Mr. Trump since his first days in office, when the president authorized an ill-fated raid on a Qaeda hide-out that left one member of the Navy’s elite SEAL Team 6 dead.