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The heads had been placed on the hood of an official car for the municipality of Tlacotalpan, along with a message containing the initials of a Mexican drug cartel. Brutal displays of gang violence are not uncommon in Mexico.
"We regret with deep sorrow the events that took place in our municipality last night," read a post on the official Twitter account of the town.
Clashes between rival drug gangs contributed to a record high number of murders in Mexico last year. Veracruz is one of the most violent states.
Murders in Veracruz rose about 35 percent through November last year compared with the same period in 2016. The state has also seen four of the 12 murders of reporters in Mexico last year.