It was unclear what the soldiers were doing in the United States, but U.S. law enforcement authorities have long said that current and former Mexican military personnel have been hired to protect drug and migrant smugglers.
"Unfortunately, this sort of behavior by Mexican military personnel has been going on for years," union Local 2544 of the National Border Patrol Council (NBPC) said on its Web page. "They are never held accountable, and the United States government will undoubtedly brush this off as another case of 'Oh well, they didn't know they were in the United States.'
"It is fortunate that this incident didn't end in a very ugly gunfight," said the local's posting.
The NBPC represents all nonsupervisory personnel among the agency's 16,000 agents.
Border Patrol spokesman Michael Friel did not return calls for comment Tuesday.
State Department spokeswoman Nicole Thompson said Tuesday that the department had no information on the incident, and referred further questions to the Border Patrol. "It is not an incident that we are aware of," she said.
Ricardo Alday, spokesman at the Mexican Embassy in Washington, said Tuesday that Mexico and the United States are engaged in "an all-out struggle to deter criminal organizations from operating on both sides of our common border."
"Law enforcement operations have led, from time to time, to innocent incursions by both U.S. and Mexican law enforcement personnel and military units into the territory of both nations, and in particular along non-demarcated areas of our border," he said.