Several left-wing Spanish politicians on Sunday demanded Prime Minister Mariano Rajoy resign after police used force to block voting in a banned independence referendum in Catalonia, injuring dozens of people.

Barcelona mayor Ada Colau said Rajoy, the leader of the ruling conservative Popular Party (PP), "had crossed all red lines".

"He is a coward who does not live up to his state responsibilities... as a result he must resign," she told reporters.

Colau demanded that police stop their crackdown against the referendum, which Spain's central government and the courts have deemed illegal.

At least 92 people were injured in Catalonia in clashes between police and protesters over the vote, two of them seriously, a spokeswoman for the Catalan government's health department said.

Spain's interior ministry said 12 police officers had been injured in the clashes.

Police have baton-charged and fired rubber bullets to disperse crowds protecting polling stations in Barcelona and other towns and cities.

Videos posted on social media show police dragging voters from polling stations by their hair, throwing people down stairs and attacking Catalan firefighters who were protecting polling stations.

"To open a new scenario of dialogue and coexistence, it is necessary to send the PP and Ciudadanos to the opposition," Pablo Iglesias, the leader of far-left party Podemos, said on Twitter in reference to the PP's allies in parliament.

"If something breaks Spain it will be because the PP and those who support it in parliament continue to destroy democracy," he added in messages accompanied by pictures of injured protesters, some of them bleeding.

Pablo Echenique, a leading member of Podemos, wrote on Facebook that the PP's policies in Catalonia, could "fracture a society and destroy a country".

"You have to remove the tumour before it kills the patient," he added.

PP spokesman Fernando Martinez-Maillo defended the government, saying that "the only ones responsible for what is happening in Catalonia today is (Catalan president Carles) Puigdemont, the government of Catalonia and its partners."