"Supporters of Daesh yesterday executed members of the Awlaki tribe after kidnapping them," a senior tribesman told AFP, using the Arabic acronym for IS.
Another tribal source said Hashem and Ahmed Maklam al-Tunssi were killed in Seiyun, the second largest town in Hadramawt province, where Al-Qaeda in the Arabian Peninsula (AQAP) has a significant presence.
The men belonged to the same tribe as US-born radical cleric Anwar Al-Awlaki, who Washington alleges was a senior Al-Qaeda operative.
The pro-government "Popular Resistance" force in Hadramawt confirmed the deaths of the two men in a statement accusing IS of the killing.
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The announcement comes a day after AQAP fighters drove pro-government forces out of a town in southern Yemen that could potentially open up a supply route between their stronghold of Mukalla, in Hadramawt, and second city Aden.
At least 15 people were killed when AQAP fighters swept into Jaar, in Abyan province, before appearing to withdraw from the town.
AQAP, which has taken advantage of fighting between loyalist and rebel forces across the country, took control today of a checkpoint in Jaar leading to the town of Zinjibar, where the jihadists already control government buildings.
The United Nations says more than 5,700 people have been killed in Yemen since then, nearly half of them civilians.