The clip shows the Wagner chief walking with his men at night, and explosions can be heard — but it is not clear where or when it was filmed.
Standing beside the body, which appears to have suffered a stomach wound, Prigozhin said: “He came to meet us. Citizen of the United States of America.”
Prigozhin shows the camera what appears to be the soldier’s identity documents, without giving a full name.
“We will return him to the United States. We will put him in a coffin (with) the American flag. With respect, because he didn’t die in a grandfather’s bed but in the war,” the Wagner boss said.
Prigozhin’s paramilitary group is fighting on the front line in the bloody battle for Bakhmut, a flashpoint town in eastern Ukraine.
AFP could not independently verify Prigozhin’s claims.