The two CIA officers received non-life-threatening wounds and have returned to the United States. The navy captain was uninjured and radioed the navy for help.
Twelve officers have been detained in the case and are being held under a form of house arrest pending possible charges, and 51 officers have testified in the case. The FBI, which is leading the investigation for the U.S., has been in on interviews of the detainees. At FBI headquarters in Washington, spokesman Paul Bresson declined to comment.
A Mexican federal police spokesman said last month that the officers may not have noticed the diplomatic plates. The official said police focused on the unusual sight of a bulletproof SUV traveling at high speed on a rural road, not on the car's distinctive diplomatic plates.
But Raul Benitez, a security expert at Mexico's National Autonomous University, said Mexican military sources have told him that "the attack was not an error," and "the objective was to annihilate the three passengers in the car."
"The same car with the same people had been going up and back (to the marine training camp) for a week, so perhaps some lookout who worked for drug traffickers informed the police, or the Beltrans" about the vehicle, Benitez said.
He said the federal police must have known that they were attacking a diplomatic vehicle.
"I don't think we're yet in a position to say definitively who did it, who paid them and why they did it," the U.S. official said. "We have been assured repeatedly in private and in public that the government of Mexico will investigate this to the end and provide a final answer as to what occurred, and I think our posture at this stage is we take them at their word."
Mexico's federal police agency, which President Felipe Calderon calls the most professional and highly trained of the country's law enforcement, has been hit with allegations of wrongdoing in recent months. In August, all 348 officers assigned to security details at the Mexico City International Airport were replaced in the wake of a June shooting of three federal policemen, who were killed by a fellow officer believed to be involved in trafficking drugs through the terminal.
Ten federal police officers were arrested in the northern border city of Ciudad Juarez in 2011, accused of running an extortion ring.
Attacks on diplomatic personnel in Mexico were once considered rare, but the CIA attack was the third shooting incident in two years.
In 2011, a U.S. Immigration and Customs Enforcement agent was killed and another wounded in a drug gang shooting in northern Mexico.
A drug-gang shooting in 2010 in the border city of Ciudad Juarez killed a U.S. consulate employee, her husband and another man.
That could be the result of the break-up of larger cartels, said Andrew Selee of the Washington-based Mexico Institute, noting that historically drug traffickers didn't want the attention that a hit on U.S. personnel normally brings.
"The lower level leaders in the cartels are making decisions the more seasoned leaders wouldn't," he said. "It's the lower level leaders who feel empowered to order hits."
Associated Press writers Mark Stevenson in Mexico City and Elliot Spagat in San Diego contributed to this report.