The pilot ejected from the flight moments before the crash and was safely rescued by US military officials, it said.
US officials in South Korea and South Korea’s defence ministry spokesperson could not immediately confirm the report.
The US military base at Gunsan airport is about 180km (110m) south of Seoul and has approximately 2,800 air force members, army soldiers and other officials at the installation.
It comes as North Korea on Monday criticised South Korea and the US for “walking on the path of confrontation and war” by staging joint military drills, according to Pyongyang’s official Rodong Sinmun newspaper.
It called the joint drills "futile" provocative acts that will only hasten the South Korea’s destruction and slammed Seoul for “recklessly” running amok to stage a war in the peninsula.
"Having the US on its back, the puppet group is pursuing an ambition for a northern invasion and walking on the path to confrontation and war. Its rash act is foolish and a futile bravado that hastens its ruin," it said.
South Korea and the US have intensified training exercises in the region in the wake of North Korea’s increasing ballistic missile tests, including the banned new solid-fuel intercontinental ballistic missile (ICBM).
Although the allies argue that the field exercises are intended for planning their response to a potential North Korean attack, Pyongyang consistently denounces them as a rehearsal for invasion and has in the past countered with missile launches.