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The video, shot in 2004, is being released in response to recent news reports that more than 200 incursions by the Mexican army have been documented since 1996.
The group says it sent footage to then-Secretary of Homeland Security Tom Ridge, but his office did not respond.
In the 2004 incident, Minuteman leader Chris Simcox and a group of volunteers said they encountered a squad of about eight armed Mexican soldiers some 500 yards inside the United States.
The Mexican soldiers ran back through the brush to Mexico when they realized they had been spotted, the Minuteman volunteers said.
In the video, a uniformed Mexican soldier is seen climbing through a barbed wire fence on American soil to return to the Mexican side and catch up with his colleagues.
The soldiers retreated up a hill to a group of abandoned buildings at a ranch where military transport vehicles with more soldiers could be seen.
Later, a group of armed Mexican soldiers returned to the barbed wire fence on American soil and confronted Simcox and the volunteers.
An agitated soldier told the Americans they had no business being there, but the Minuteman members did not move. The soldiers then drove off.
Simcox believes, based on earlier activity observed at the ranch, that the volunteers had disrupted a trafficking operation.
The Minuteman volunteers have been called vigilantes by President Bush, but, as WorldNetDaily reported, in September a Rasmussen poll indicated 54 percent of Americans approve of them.