The violence damaged the city hall, a court and the police headquarters in Padilla, a town just north of the Tamaulipas state capital of Ciudad Victoria, the state government said in a statement.
Seven bodies were dumped in Padilla's main square on Monday, another five people were shot to death inside their car, and another person was killed in an attack on a passenger bus, the statement said. Five other inhabitants of the town were killed, but the statement did not specify how.
Tamaulipas, a state bordering Texas, has seen some of the worst atrocities in Mexico's drug war since fighting broke out last year between the Gulf cartel and a gang of its former enforcers known as the Zetas.
Nearly all inhabitants fled one small, picturesque town in the Rio Grande Valley after months of gang battles. In the worst massacre, 72 Central and South American migrants were found bound and shot to death in Tamaulipas ranch in August. Authorities say the Zetas killed the migrants for refusing to work for the gang.
The Tamaulipas government said innocent bystanders were among the dead in Padilla, but it did not specify how many. The statement expressed "solidarity with the families of the innocent victims."
In neighboring Nuevo Leon state, meanwhile, gunmen killed a top intelligence officer, then torched his car, the state government said in a statement.
Homero Salcido Trevino's body was found in a smoldering car abandoned in downtown Monterrey, Mexico's once-peaceful third-largest city that has also been besieged by the Gulf-Zetas fighting.
Salcido Trevino was the director of the state's intelligence and security center, a job he had taken in August. He was shot at least five times, said the statement, which offered no additional details.
The attack had some of the hallmarks of a drug cartel hit, but Nuevo Leon Gov. Rodrigo Medina said investigators had not confirmed that. "It is still premature to tell you it was organized crime," he said.
Local news media reported that Salcido Trevino, who was the nephew of former state Public Safety Secretary Luis Carlos Trevino Berchelmann, had been kidnapped hours earlier as he left his home. Authorities would not comment on the reports.
Gang members have fiercely attacked police and soldiers trying to restore order across Nuevo Leon and Tamaulipas. Police, mayors - and even the leading gubernatorial candidate in Tamaulipas - have been assassinated in more than a year of violence.
Killings soared in Nuevo Leon state last year to 620, compared to 112 in 2009.
"What is evident is that we have a vicious fight between the cartels of organized crime, which have provoked this violence and has obligated us to redouble our efforts," Medina said.
Medina said security officials know the risks they face. He vowed attacks will not "force us to back down or stand aside in this fight."
The Defense Department, meanwhile, announced the capture of a top Zetas suspect.
Juan Carlos Olivera, allegedly the top Zetas operator in five towns around Monterrey, was arrested with two accomplices and four guns, the department said in a statement.
Nationwide, almost 35,000 people have been killed in drug violence since President Felipe Calderon launched a military crackdown against drug trafficking shortly after taking office in December 2006.
In the Pacific coast resort city of Acapulco, police discovered three dead men from a car left in the parking lot of a state prison Sunday, authorities said Monday. A fourth man was found alive in the car with bullet wounds in the face and neck, Guerrero state police said.
A dozen people were killed in Acapulco over the weekend, including a prison guard, authorities said.