A car bomb exploded Saturday in the central state of Hidalgo, killing a police commander and wounding three officers.
State Public Safety Secretary Damian Canales Mena said the officers were checking out a tip that a body was in the trunk of the vehicle when it exploded.
Investigators suspect the Zetas drug cartel was behind Saturday's attack in the town of Tula. It could be revenge for the recent killings of several cartel members by police, Canales Mena said.
Hidalgo is the home state of alleged Zetas leader Heriberto Lazcano Lazcano and a central transit point for drugs.
In Chihuahua state, meanwhile, authorities said a commander who worked in internal affairs for the local Attorney General's Office was killed along with another agent.
State Attorney General's Office spokesman Carlos Gonzalez said the two were gunned down Friday afternoon in the capital, also called Chihuahua. A third agent was gravely wounded. A motive was not immediately known.
And in nearby Ciudad Juarez, across the border from El Paso, Texas, three men died when a gasoline bomb was thrown into their store.
State prosecutors also said that elsewhere in Ciudad Juarez, authorities found the dead bodies of three other victims of apparent gangland murders.
The Sinaloa and Juarez cartels have been fighting for control of the lucrative trafficking routes in Chihuahua.
More than 34,600 people have died in drug-related killings in Mexico in the four years since President Felipe Calderon launched an offensive against the cartels.
