Conistorgis was the main city of the Conii or Cynetes. It was located somewhere in the interior of the Algarve, in southernmost Portugal, although the exact location is unknown. In the Conii language it probably meant "city of the Conii". The Celtici seem to have been present there.
The Conii had made an alliance with the Romans during the conquest of the Iberian Peninsula. This led to the city's destruction by the indigenous Iberian confederation, led by the Lusitanians, during the Lusitanian War against Rome.