"Organized crime has sparked a serious problem of violence in Veracruz," said the state's governor Miguel Angel Yunes in a statement, calling the latest violence "an act of terrible barbarism."
Among Saturday's victims were a federal police commander and two agents, who were ambushed by gunmen in the city of Cardel.
In the nearby city of Coatzacoalcos, the dead included two adults and four children who died in a hail of bullets as they ate dinner at an outdoor restaurant.
Much of the violence is the result of turf battles between two rival drug trafficking gangs, the Zetas and Jalisco Nueva Generacion.