The disclosure came a day after the incident left two people dead and two wounded on an isolated gravel road near the town of La Joya, just north of the Mexico border.
The pickup truck was first encountered Thursday by state game wardens, who believed it was occupied by illegal immigrants. When the driver refused to stop, the game wardens radioed for help, and a state police helicopter with a sharpshooter was the first to respond, according to Texas Parks and Wildlife Department spokesman Mike Cox.
In a statement, the Texas Department of Public Safety said the truck appeared to be a carrying a "typical covered drug load" on its bed and was travelling at reckless speeds.
After the shots were fired, the truck stopped. Seven Guatemalans were arrested, and no drugs were found.
The nationalities of the dead and of an eighth person arrested later were not immediately released.
The officer who fired the shots has been placed on administrative leave, which is standard procedure in fatal shootings.
In recent years, Texas state police have increased their presence in the border area, deploying more agents, more helicopters and more boats to patrol the Rio Grande.
Troopers are regularly involved in high-speed pursuits, often chasing drug smugglers into the river and back to Mexico.
Agency Director Stephen McCraw has said state police were pushed into that role because the federal government's efforts to secure the border have been insufficient.
Diplomats quickly began their own investigation into the chase.
Rita Claverie, Guatemala's deputy minister of foreign relations, said her government will demand an explanation from the U.S.
"This incident surprises us because we had never seen force being used from a helicopter. ... What had happened in the past were car pursuits and, in some cases, the shooting of undocumented persons," Claverie said.
Humberto Palacios head of protection and investigations at the Guatemalan consulate in McAllen, said the consulate was looking into the matter and would ask authorities to establish what happened.