American officials and analysts said the Qaeda leader who was believed to have been killed was Abdulrauf al Dhahab.

The raid took place in Yemen around the time that Mr. Trump was signing a directive in Washington on Saturday afternoon ordering Defense Secretary Jim Mattis to devise within 30 days a more aggressive plan to defeat the Islamic State.

The Islamic State was born from Al Qaeda’s branch in Iraq, but the two terrorist organizations are now sworn rivals not only in Iraq and Syria, but also in other hot spots like Yemen and Afghanistan, where both groups have affiliates.

Because Mr. Trump had been explicit about his intention to ask for the review to accelerate the fight against the Islamic State, also known as ISIS or ISIL, American military planners had begun drafting classified options to present to the new commander in chief. Some of those options, like pushing more authority to conduct strikes to commanders in the field or loosening restrictions designed to limit the risk to civilians, could also be applied to attacks against Qaeda fighters and Islamic State insurgents.

There were no immediate indications that the rules of engagement had been loosened for the mission in Yemen, military officials said. The Central Command’s statement did not elaborate on details of the raid or identify the commando who was killed.

A local resident who witnessed the raid, speaking by phone, said he had seen warplanes bombing several houses in the village around 2 a.m. Sunday. The man said he had seen at least three buildings being struck before he fled. He did not want to be identified because he feared that speaking out would endanger his life.

A Yemeni government official in Bayda Province said the targeted buildings belonged to the Dhahab family, which is known for its ties to Al Qaeda. Two male members of the family have been killed in drone strikes over the past two years.