A spokeswoman for the city's health authorities declined to say when Father Pajares, who was airlifted from Liberia last week after contracting the disease while working for a non-governmental organisation in the African country, had died.
The priest was being treated in the Carlos III hospital, where he had been in quarantine since his return from Africa.
The Health Ministry said he was being treated with the experimental drug ZMapp, manufactured by US company Mapp Biopharmaceutical. Two US aid workers infected with the disease have shown some signs of improvement since being given the drug.
Father Pajares was repatriated with co-worker Juliana Bohi, a nun who has tested negative for Ebola.
A World Health Organisation panel of medical ethics experts yesterday ruled it was ethical to offer unproven drugs or vaccines as potential treatments or preventions in West Africa's deadly Ebola outbreak.
The UN health agency said provision of experimental Ebola drugs required "informed consent, freedom of choice, confidentiality, respect for the person, preservation of dignity and involvement of the community".
The panel met to discuss whether various experimental medicines and vaccines being developed for Ebola might be used in the outbreak, despite not having been fully tested or licensed.
The meeting was called after ZMapp was given to the two American health workers infected with Ebola in Liberia.
The panel said in a statement: "Ebola outbreaks can be contained using available interventions like early detection and isolation, contact tracing and monitoring, and adherence to rigorous procedures of infection control. However, a specific treatment or vaccine would be a potent asset to counter the virus."