"The aircraft had a crew of four and was out on a training mission in Nordland County" in northern Norway, according to a statement.
It was on its way north to Bodø, where it was scheduled to land just before 6pm on Friday. The plane crashed in Gråtådalen in Beiarn, south of Bodø. Police said a search and rescue mission was launched immediately. At 1.30am Saturday, the police arrived at the scene and confirmed that the crew of four had died.
The annual Nato drills in Norway are unrelated to the war in Ukraine. This year they included around 30,000 troops, 220 aircraft and 50 vessels from 27 countries. Non-Nato members Finland and Sweden are also participating.
The exercises began on March 14 and ends on April 1.
No cause was given for the crash, but the Norwegian armed forces said Cold Response "will carry on as planned, with the measures we have to take due to the weather".