The incident has sparked a rally in Madrid to protest at his death, which has been blamed on the Basque separatist group Eta.
Raul Centeno’s colleague Fernando Trapero was also shot in the head and has been comatose since the attack, which took place on Saturday.
All the mainstream parties had called upon Spanish people to support the rally although the prime minister was conspicuous by his absence.
Boos were heard for Prime Minister Jose Luis Rodriguez Zapatero at the funeral of the dead police officer on Sunday, and the sounds of disapproval were made by those who accuse the Spanish leader of appeasing Eta.
Jose Luis Rodriguez Zapatero was in talks with the organisation last year but an Eta bomb subsequently killed two people in a Madrid airport car park last December and, then in June, Eta officially ended its ceasefire.
