Francisco Javier Dominguez-Rivera, 22, of Puebla, Mexico, was killed Friday in a confrontation with the unidentified agent north of the U.S.-Mexico border between Bisbee and Douglas.
On Sunday, Calderon expressed his "most energetic protest" against the shooting.
A group of seven people were crossing the desert and the agent took six of them into custody without incident, authorities said.
But the agent and Dominguez-Rivera began fighting, authorities said. The agent, who believed his life was in danger, shot and killed the man, the Border Patrol said previously. An autopsy was scheduled Wednesday.
The agent was put on paid administrative leave pending the investigation.
FBI spokeswoman Deborah McCarley and Gustavo Soto, a spokesman with the U.S. Border Patrol Tucson sector, both declined Monday to provide details of the case.