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Mr. Friel noted that the ongoing construction of 670 miles of fencing along the southwestern border “will result in a clearer delineation of the international border” and a reduction in the number of incursions.

Last week, the State Department and the Border Patrol in Washington described the Aug. 3 incursion as a “momentary misunderstanding,” saying the Mexican soldiers did not know where they were and needed to make certain that the detained agent was who he said he was - although rank-and-file Border Patrol agents in Arizona said he was dressed in uniform and was driving a well-marked, white-and-green agency vehicle.

The incident occurred on the Tohono O’odham Indian Reservation, a major corridor for smuggling humans and drugs.

Mr. Tuffly said the four Mexican military personnel who crossed into the United States on Aug. 3 did so after passing vehicle barriers that Homeland Security had erected at the border. The agent was in full uniform and was driving a fully marked Border Patrol vehicle, complete with red and blue lights, large green stripes down the side, and the large words “Border Patrol” on the sides and the rear of the vehicle, he said.

“A reasonable person would conclude that the soldiers knew exactly at whom they were pointing their rifles,” Mr. Tuffly said. “Had the agent panicked and fired a shot or attempted to flee in his vehicle, there is little doubt the Mexican soldiers would have opened fire.”

He described the State Department’s declaration that the incident was a “misunderstanding” as “unfortunate.”

“During past incursions, the Mexican government has denied it had soldiers in the area. They have blamed impostors, even when military Humvees were involved,” he said. “Time after time they have gotten away with these incursions and time after time our government has not taken a forceful stand against them.”

Mr. Hunter said in his letters that 43 Mexican military incursions have been reported in the past 10 months and more than 200 since 2006. In the letter, he asked what action the Homeland Security and State departments were taking “to address the incursion … and limit or prevent the likelihood of similar incidents in the future.”