The cleric, Harith bin Ghazi al-Nadhari
, was killed in Yemen's south-central Shabwa province, AQAP said.
The strike would be a further indication that a U.S.-led drone strike program is continuing following a pause during political upheaval in the majority Sunni Muslim nation.
The United States has long conducted drone strikes against AQAP targets under the Obama administration. But the New America Foundation
, which tracks the strikes, says there was a nearly two-month pause in the strikes in late 2014 and early 2015
as Shiite Muslim Houthi rebels moved against Yemen's U.S.-backed government.
That uprising culminated in the resignation of Yemeni government's top leaders in mid-January. A week later, the U.S. drone strikes resumed, with a strike east of the capital, Sanaa
, three U.S. officials said at the time.
Al-Nadhari made headlines in November when he inserted himself into a rivalry between al Qaeda and ISIS
, or the Islamic State in Iraq and Syria.
ISIS has captured parts of Syria and Iraq for what it calls its Islamic caliphate. In mid-November, ISIS leader Abu Bakr al-Baghdadi issued an audiotape saying his Islamic State had expanded to Yemen and other Middle Eastern countries.
Al-Nadhari responded harshly in a video a week later, saying al-Baghdadi's declaration of an Islamic caliphate was illegitimate.
"Our brothers in the Islamic State ... surprised us with several steps, including their announcement of the caliphate (and) they announced the expansion of the caliphate in a number of countries which they have have no governance, and considered them to be provinces that belonged to them," al-Nadhari said, according to a translation by the SITE intelligence group.
"The announcement of the caliphate for all Muslims by our brothers in the Islamic State did not meet the required conditions," al-Nashari argued, because other jihadi groups were not consulted.
Al-Nadhari also criticized ISIS for "going too far in interpretations in terms of spilling inviolable blood under the excuse of expanding and spreading the power of the Islamic State."
ISIS and al Qaeda's top leadership in Pakistan had a bitter falling out in 2014, and al Qaeda and ISIS fighters have been fighting each other in Syria, but AQAP until November had stayed above the fray, calling for both sides to reconcile and pool resources to strike the United States.
Journalists' group: Houthis attacked newspaper office
Houthi militants dressed in government uniforms raided the main office of Yemen's daily Akhbar Al Youm newspaper Thursday, according to two officials in the Yemen Journalists Syndicate, an organization for reporters in the country.
Eyewitnesses said the attackers damaged some equipment and forcefully locked some journalists inside a guard room at the office. Details about how long the journalists allegedly were detained weren't immediately available.
Akhabar Al Youm is one of the oldest independent publications in Yemen, with print houses in Sanaa and Aden.
Houthi officials did not confirm that Houthis were involved in Thursday's raid. However, Ahmed Al Bahri, a legal adviser for the Houthis, said the newspaper had "always been anti-Houthi" and is funded by those who oppose the minority group.
"Many lies against the Houthis are published, which in return damages our reputation, and with no government censorship over its reporting," Al Bahri said.