It is one of the most famous Islamic sites in Europe, but those coming to learn about that are left none the wiser by the information leaflets given out to tourists, critics say.
"For the citizens of Cordoba, what has hurt our feelings is that they have cut off the name and the memory of the monument," said Antonio Manuel Rodríguez, a law professor at Cordoba University.
He is a member of a secular group of local campaigners who have gathered 146,000 signatures on a petition demanding that the common Islamic and Christian heritage of the site be recognized.
The acclaimed British architect Norman Foster is among the signatories, as well as many Spanish writers and scientists and moderate Catholics.
A historical jewel in the southern city that was a capital of Islamic Spain in the Middle Ages, the building with its cobbled patios and minaret draws more than a million visitors each year.
The entry ticket visitors receive bids them "welcome to the Santa Iglesia Cathedral", but does not mention that the building, now administered by the church, was a mosque for centuries.
"Over the past few years, the Diocese of Cordoba has erased the term 'mosque' from all the information leaflets of what is recognized worldwide as a symbol of cultural harmony," the "Save the Cordoba Mosque" petition says.
This "offers millions of tourists a distorted historical account, which crudely adulterates the essence of a complex building and an emblem of diversity."
Andalusia's golden age
The visitors' leaflets point out that a mosque was built on the site of a Visigoth church in the eighth century, but skims over its next 500 years as a place of worship for Muslims at the height of the Islamic rule in southern Spain.
UNESCO, in its listing of Cordoba's historic centre as a world heritage site, highlighted its place in the Andalusia region's golden age, which began with its conquest by the Moors in the eighth century.
Under the Islamic Umayyad rulers, Cordoba flourished with mosques and palaces that rivalled Constantinople, Damascus and Baghdad for splendour, UNESCO said.
Construction of the mosque, with its grand prayer room and marble columns, began in 766. It was transformed to a cathedral in the 13th century after a Christian ruler conquered the city.
In 2006, the campaigners say, the Cordoba bishopric registered the cathedral as its own property without informing the regional government which had allowed the Church to run the site.
Until that point, the site "was in legal limbo -- it was neither public nor private property", said Rodriguez.
"The problem arises when the Church hierarchy thinks it belongs to them," he added.
Andalusia's Socialist regional government said last week it was considering legal action "to protect the public ownership of this cultural asset".
The Cordoba diocese insists that it "always had understanding and loyal collaboration with the public administration, never questioning the ownership nor the running of the place of worship".
The Church, which was a powerful force in Spain during the four-decade Franco dictatorship that ended in 1975 -- and still pulls weight in the governing conservative Popular Party -- has its supporters in the Cordoba row.
A conservative pressure group, HazteOir, has accused the region's government of wanting to "expropriate" the cathedral.
That group has created its own petition, so far signed by more than 96,000 people, demanding that the regional government drop its efforts to keep control of the site.