Acuna Public Safety Department said in a statement that the three were on patrol in the same unit when gunmen kidnapped them early Monday.
The officer's bodies were found an hour later in a residential area of Acuna, which is across the border from Del Rio, Texas. They had been shot and their hands were handcuffed, the police department said.
Authorities say the Zetas and the Sinaloa drug cartels are fighting each other to control smuggling routes in the state of Coahuila, where Acuna is located.
Last week, gunmen killed a federal prosecutor for the state of Coahuila when he was about to leave his home in the city of Torreon.
A day earlier, gunmen set a fire at the office of the Torreon newspaper El Siglo and fired shots at it. No injuries were reported.
Authorities in the neighboring state of Durango said soldiers dug up the remains of seven people from a pit.
Durango state prosecutors said troops found the remains in the town of San Juan del Rio, about 60 miles (100 kilometers) north of the state capital, the city of Durango. They gave no other details.
More than 400 bodies have been found in a series of clandestine graves in Tamaulipas and Durango states since April. They are believed to be a result of turf battles between drug cartels.
In Hidalgo, the home state of Zetas leader Heriberto Lazcano, state police chief Damian Canales said authorities detained eight local police officers for allegedly working for the Zetas.
Canales said six of those detained were officers for the town of Actopan and two for the state capital of Pachuca. He said they were detained after the arrest of the former police chief in the town of Arenal, who authorities allege was in charge of recruiting police officers to work for the Zetas.
Canales said the Pachuca city police officers told investigators the Zetas paid them about $360 a month.
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