Evidence "indicates that it was a confrontation between two groups," according to President Andres Manuel Lopez Obrador (AMLO).
The confrontation took place in a remote area of the Miguel Aleman municipality Wednesday morning. The bodies and several burned-out vehicles were found by the authorities that afternoon.
Attorney General of Tamaulipas Irving Barrios Mojica said that along with the 21 bodies, the torched remains of four pick-up trucks and a car were also found.
Preliminary investigations found bullet shells from AK47 rifles, Barrets and .50 calibers, but no indication of how many people were involved in the confrontation.
According to local media, some of the bodies found near the Los Portones town had bulletproof vests and clothes with military-like camouflage painted on it.
Police were tipped off by the wife of one of the victims who reported her partner as missing and said they could find him in Miguel Aleman.
The clash is believed to have been between members of the Gulf Cartel and the North-East Cartel, both prominent in the drug crime and violence consuming Mexico.
"What we can assume is that there was a winning group in that battle that set fire to vehicles and bodies," said Barrios.
Tamaulipas state, known as 'La Frontera Chica' (small border), has one of Mexico's highest rates of trafficking in drugs, weapons and people. For years it was controlled by the Gulf Cartel and its armed wing, Los Zetas, but in 2010 the cartel split, sparking a bloody war for control of the zone.
According to the National Public Security System (SNSP) and local civic organizations, Tamaulipas also has one of the highest violence rates but has been named a 'Silence Zone' by journalists who prefer not to cover the violence due to repeated threats.