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Fighting erupted on Sunday in two villages called Amchaloka et Amsabarna in Sila province and continued on Monday, they said.
Separately, a hospital worker put the toll at 21 dead and 29 wounded.
Twelve people were killed on Thursday in the neighbouring province of Ouaddai when a village was attacked by armed men, provincial public prosecutor Hassan Djamouss Hachimi said.
"We arrested 30 people," he said.
Eastern Chad is grappling with tit-for-tat violence between native Ouaddian farmers and Arab herders, an issue raised during a visit to the region in February by President Idriss Deby Itno.