Marines on patrol Tuesday afternoon near the town of San Fernando were attacked by armed assailants travelling in several vehicles, the state government said in a statement issued Thursday.
The marines returned fire, killing five of the attackers.
The troops also seized an SUV with Texas licence plates as well as a small arsenal that included five rifles, a handgun, a grenade launcher and four projectiles and 974 rounds of ammunition.
Also Tuesday, marines deployed in the border city of Matamoros, just across the Rio Grande from Brownsville, Texas, spotted four armed men travelling in an SUV and ordered them to stop.
The men started shooting at the marines in an attempt to flee, according to the official statement. A man was killed in exchange of fire and another was found dead in the passenger seat of another SUV.
Tamaulipas has been the scene for several years of violent conflict between the rival Gulf and Zetas drug cartels and between the criminals and security forces.