We have implemented Allah's ruling against them, which is the death sentence, says al Qaeda statement. PHOTO: AFP
Residents of Mayfaa town in the southeastern province of Hadramawt said al Qaeda militants had distributed a pamphlet naming the four men.
It did not say when the killings were carried out, but a neighbour of one of the victims told AFP that he had been missing for days.
"We have implemented Allah's ruling against them, which is the death sentence," said the flier that was also posted on walls in the area.
"We call upon all Muslims to cooperate with us against this widespread depravity," it said.
Read: 'Witch' killings haunt India's remote villages
Al Qaeda in the Arabian Peninsula, or AQAP, has overran large parts of Hadramawt, including Mukalla, the coastal provincial capital.
It imposed a strict version of Islamic law, executing or lashing those they accused of various crimes, among them homosexuality and sorcery. Those accused of theft have their hands cut off.
The United States considers AQAP as the most dangerous affiliate of the militant network.
It is active across several parts of Yemen, taking advantage of a collapse of central authority during a 2011 uprising that ousted veteran president Ali Abdullah Saleh.
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