Mayor Hector Murguia and the federal police had conflicting accounts of what led to the Tuesday night shooting, and four federal agents were being interviewed Wednesday by the Chihuahua state prosecutors' office to try to determine responsibility.
Murguia said his bodyguards were outside a house where he was holding meetings when two masked federal police officers approached. He said his guards identified themselves but the federal police shot one of them anyway.
He identified the slain bodyguard as Jose Humberto Perez, 29, a city policeman assigned to the mayor's security.
"I am so furious and indignant ... about the killing of this young man for no reason," Murguia said. "If this is the way it is with the mayor, how must it be with regular citizens?"
The Public Safety Department, which oversees the federal police, said the guards refused to identify themselves and acted belligerently, pointing their guns at the federal agents, who opened fire.
"The guards were wearing civilian clothing and at no moment did the guards obey the order to identify themselves and lower their weapons," the department said in a statement on Wednesday.
The department said the federal police approached the house after receiving a report from a taxi driver about the presence of armed men there.
The statement did not identify the federal police involved in the shooting but said they and their weapons were turned over to Chihuahua state prosecutors for investigation.
Mexico's federal police are largely responsible for security in Ciudad Juarez, one of the most dangerous cities in the world due to a fierce turf war raging between the Sinaloa and Juarez drug cartels.
The shooting stoked tensions in a city where many citizens are already angry that violence has only increased since the federal government deployed troops and federal police two years ago. More than 3,000 people were killed last year in the city of 1.3 million across the border from El Paso, Texas.
Murguia was inside the house when the shooting took place, and his life was not in danger. The house where the shooting occurred is near a hotel where the federal police are housed.
Murguia said he went to the hotel after the shooting to demand an explanation but the federal police there dismissed him with aggressive words.
"This is a very difficult situation," Murguia said. "It can't be that a masked assassin goes out and kills like this."