There were around 400 passengers and staff on the two trains, operated by Iryo and Renfe, according to a statement from Renfe.
It is not clear if there are people still trapped inside the carriages but rescue teams are on site.
“The problem is that the carriages are twisted, so the metal is twisted with the people inside,” Francisco Carmona, head of firefighters in Córdoba, told Spanish public broadcaster RTVE.
“We have even had to remove a dead person to be able to reach someone alive. It is hard, tricky work,” he added.
The president of the Andalusian regional government, Juanma Moreno, told local outlet Canal Sur that they are waiting for “heavy machinery” to “practically lift” parts of the second train, which “has taken the worst part of this accident”.
“Until the heavy machinery can do its job and free the wagons from the track”, emergency services will not be able to start “searching and identifying” any remaining victims, he added.