The shooting left a bullet impact on the auto window while the United States consular official is seen opening his door.
The FBI has asked anyone with information to contact the U.S. Embassy in Mexico Cityat (01-55) 5080-2000.
Mexican and U.S. officials appealed to the public on Saturday for help in finding the gunman who wounded the official earlier that day. One showed the man in the purple shirt in greater detail - and wearing dark sunglasses - as he ran behind a truck. That information blackout included the man's condition; however, Mexico's attorney general said the victim was in "stable" condition and under protection.
In 2012, two USA government officials - widely reported to be CIA agents - and a Mexican marine where wounded in 2012 when they were shot at by federal police officers as they were driving in the central state of Morelos.
The Guardian, citing a source within the Guadalajara police, said Mexican cops found Drug Enforcement Administration (DEA) credentials in Ashcraft's name after the shooting. The gunman is then seen following him. As the auto drove up, the man pulled out a gun and shot the person in the vehicle.
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The western city of Guadalajara has been hit by violence perpetrated by the powerful Jalisco New Generation drug cartel in recent years. "US government personnel are authorized to use Federal toll road 15D for travel to Mexico City; however, they may not stop in the town of La Barca or Ocotlan for any reason".
The State Department did not have a travel warning out for Guadalajara, though Mexican gangs and cartels have targeted US officials before.
The U.S. Embassy in Mexico issued a safety warning after the shooting, urging American citizens in the Guadalajara area to restrict their movements outside their homes and places of work.
Partlow reported from Mexico City.