Patrick White, who was driving in the area at the time of the crash, said he saw the aircraft trailing low to the ground, kicking up a cloud of dirt and dust.
He said it briefly disappeared from his line of sight, before he saw “an enormous plume of black smoke”.
When he drove past the crash, Mr White said he saw a piece of the fighter jet in the middle of the road.
It marks the second crash of a military plane in New Mexico in the past month.
In April, an F-16 Fighting Falcon went down in a remote area near Holloman Air Force Base in the southern part of the state, leaving the pilot with minor injuries after he ejected from the aircraft.
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The conviction of dozens of civilian supporters of Imran Khan, the former Pakistani leader, in the country's military courts is of "deep concern"
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