Mexico's attorney general's office could not immediately confirm the reports of the grisly discovery in Mante and police officials in the crime-ridden city were not immediately available for comment.
Mexican media said the body parts belonged to 10 men and four women and the message was directed at the Gulf cartel.
In a separate incident on June 7, 14 dismembered bodies were discovered inside a truck in Mante, located in the south of Tamaulipas state, which borders Texas and is one of the bloodiest battlegrounds in Mexico's drug war.
More than 55,000 people have been killed in the conflict since President Felipe Calderon sent in the army to fight drug gangs shortly after he took office in December 2006.
Calderon's conservative National Action Party, or PAN, appears likely to lose power in the presidential election on July 1, due partly to rising frustration with the drug-related violence.
This week, Mexico was left red-faced after authorities admitted they had mistakenly claimed to have captured a son of the country's most-wanted man, drug lord Joaquin "Shorty" Guzman.