Twelve were in intensive care after the accident near Adamuz in the province of Cordoba, about 360km south of Madrid, according to emergency services.
Experts say a faulty rail joint might be key to determining the cause of the crash.
"The train tipped to one side ... then everything went dark, and all I heard was screams," said Ana Garcia Aranda, 26, who was being treated at a Red Cross centre in Adamuz.
Limping and with plasters across her face, she described how fellow passengers dragged her out of the train covered in blood.
Firefighters rescued her pregnant sister from the wreckage and an ambulance took them both to hospital.
"There were people who were fine and others who were very, very badly injured ... you knew they were going to die, and you couldn't do anything," she said.
The collision occurred in a hilly, olive-growing region accessible only by a single-track road, making it difficult for ambulances to reach the area, Iñigo Vila, emergency director at the Spanish Red Cross, told Reuters.
The Andalusia region's president Juan Manuel Moreno said at least 40 people had perished, and emergency crews faced difficulties bringing in the heavy equipment needed to lift the wreckage and reach those still lying beneath it.
Prime Minister Pedro Sanchez cancelled his trip to the World Economic Forum in Davos, Switzerland and Transport Minister Oscar Puente visited the site on Monday.
Police drone footage showed how the trains came to a standstill 500 metres apart.
One train's carriage was split in two, and the locomotive was crushed like a tin can.
Experts studying the crash site found a broken joint on the rails, which created a gap between the rail sections that widened as trains continued to travel on the track, according to a source briefed on initial investigations.
That faulty joint could prove important in identifying the cause of the accident, the source said.
Ignacio Barron, head of Spain's Commission of Investigation of Rail Accidents (CIAF), said on RTVE: "What always plays a part in a derailment is the interaction between the track and the vehicle, and that is what the commission is currently (looking into)."
Paqui, an Adamuz resident who rushed to help rescue survivors with her husband, said he had "found a dead child inside, another child calling for his mother. You're never ready to see something like this."
Police said they had opened an office in Cordoba for relatives to provide DNA samples to help identify the dead.
The Iryo train was travelling at 110km/h from Malaga to Madrid when it derailed, Renfe President Álvaro Fernandez Heredia said on radio station Cadena Ser.
Twenty seconds later, the second train, heading to Huelva at 200km/h, either collided with the final two carriages of the Iryo train or with debris on the line, he said.
The Iryo train lost a wheel that has not yet been located.
It was too early to talk about the cause but it happened in "strange conditions," Fernandez Heredia said, adding that human error was virtually ruled out.
The death toll was among the top 20 highest from a train crash in Europe in 80 years, according to Eurostat data, and the highest in Spain since 2013, when a train derailed in the northwestern city of Santiago de Compostela, killing 80.
Spain's high-speed railway network is the largest in Europe and second-largest in the world after China with 3,622 km of tracks, according to Adif.
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