The rank of the military member killed in combat remains unclear, CNN reported citing an anonymous US defense official.
Earlier in the day, US Secretary of Defense Ashton Carter confirmed that enemy fire killed a military man in combat near Iraqi city Erbil.
Kurdistan Region Security Council announced on Tuesday that the Daesh sent three car bombs to occupied Iraqi towns Tel Isqof and Musqelat near Mosul, which later have been freed by Peshmerga forces aided by the US-led coalition against the terrorists.
"My heartfelt condolences are with the families of our fallen Peshmerga and the brave US serviceman martyred earlier today," he said.
The US-led coalition of more than 60 nations has been carrying out airstrikes against the Daesh in Syria and Iraq since summer 2014.
The Islamic State, also known as Daesh, is a terrorist group outlawed in the United States, Russia and numerous other countries.
