The military statement did not describe specifically what the soldiers saw the Kurdish troops do.
The detainee's death is under investigation, according to a military statement.
A separate military statement on Saturday used slightly different numbers.
North of the city, an American soldier was killed when a homemade bomb hit his vehicle, according to a military statement.
A military statement said one had been killed at an unidentified location in northern Iraq after a convoy attack.
An Israeli military statement said those to be released were "without blood on their hands."
A military statement said it was a suicide attack.
A military statement did not say when the attack occurred.
A military statement on the operation did not give more details.
Six of the eight died from explosions near their vehicles, according to an American military statement.