Hassan Khidr, a resident reached by telephone as he fled the area with help from an Arab neighbor, said a handful of local residents had converted in an effort to save themselves. When the village’s elders found out, they killed three of them, he said.

That news enraged the ISIS fighters, “so they stormed the village and started killing its people,” he said.

Mr. Khidr’s hand had been wounded in the attack, and he had played dead until he was able to sneak away, he said.

The Arab man helping him flee said ISIS had surrounded two Yazidi villages and given them until Friday to convert to Islam. Residents of one village had fled, he said.

“But the time ran out for Kocho, so the gunmen from the Islamist State stormed it and killed their men,” said the man, who gave only his first name, Abdel-Raham, because he feared retribution by the militants.