The statement did not specify whether it was police bullets that wounded the three victims
Mexican federal police shot at a US diplomatic car as they chased criminals south of Mexico City, in a chaotic incident that left two US embassy employees wounded.
The two staffers were given medical treatment and were in stable condition Friday, the Mexican and US governments said in separate statements. A Mexican navy captain who was with them suffered light injuries.
A US embassy statement said the diplomatic car was "ambushed by a group of individuals." But it added that the Mexican government also admitted that federal police shot at the vehicle and detained officers who were involved.
The Mexican attorney general's office said 12 federal police agents were questioned.
Federal police officers were conducting anti-crime operations in the area when the incident took place, the Mexican navy and public security ministry said in a joint statement.
The US embassy car was on a dirt road, heading towards a military installation in El Capulin when it was approached by a vehicle whose unidentified passengers displayed weapons.
"The driver of the diplomatic vehicle used evasive maneuvers and when it returned on the highway, the passengers in the attacking vehicle opened fire on the diplomatic vehicle," the statement added.
"Moments later three other vehicles joined the chase and shot at the US embassy vehicle."
The Mexican government statement did not specify who the four attacking vehicles belonged to, or whether it was police bullets that wounded the three victims.
It said, however, that the US diplomatic car "was hit by multiple bullets from personnel of the federal police on the Tres Marias-Huitzilac highway."
Photos at the scene showed an SUV with diplomatic plates riddled with bullet holes and its tires blown out.
The US embassy said the trio were driving to a training facility when they were ambushed.
"The vehicle attempted to escape, was pursued and sustained heavy damage," the statement said.
"The government of Mexico has acknowledged that members of the federal police were involved and fired on the US Embassy vehicle. The government of Mexico has begun an investigation and detained members of the federal police who were involved."
The shooting took place in the state of Morelos, which has suffered a surge in murders in recent weeks amid a turf war between drug cartels. The bodies of four women were found on another highway near Cuernavaca last week.
Mexico is in the throes of a violent drug war that has left more than 50,000 people dead since President Felipe Calderon deployed soldiers to combat cartels in 2006.
The United States cooperates closely with Mexico under the $1.6 billion Merida Initiative, which provides training for Mexican law enforcement officials as well as equipment to combat drug trafficking.
Mexican Interior Minister Alejandro Poire voiced deep regret over the incident, pledging to "shed light into what happened" and determine who was responsible.
The US State Department said in a brief statement that the two embassy employees had received "appropriate medical care and are in stable condition."
"We are working with Mexican authorities to investigate an incident this morning in which two employees of our embassy in Mexico City came under attack by unknown assailants," said State Department spokeswoman Victoria Nuland.
After the shooting, the army and the police closed a 10-kilometer stretch of highway as well as access to a wooded area around the scene of the incident near the town of Tres Marias.
The incident came 18 months after two US Immigration and Customs Enforcement (ICE) agents were shot while driving in a car between Mexico City and the northern city of Monterrey in February 2011.
One of the agents, Jaime Zapata, died in the attack by members of the feared Los Zetas cartel.