Among the fans, parasols and knick-knacks in the gift shop of the Santa María la Blanca museum are bottles of kosher wine and tiles painted with menorahs and magens David.

They are testament to the fact that, despite its name – not to mention its incarnations as a church, a barracks and a warehouse – the museum began its life in the 12th century as Toledo’s main synagogue.

Today, the mudéjar masterpiece is one of city’s most popular tourist attractions, a building whose walls and pillars reflect the interplay of three different cultures: Christian, Jewish and Islamic.

Visitors armed with selfie sticks and headsets mill between its white horseshoe arches, peering down at the tiled floor or up at the cherubs and christograms that sit alongside the geometric patterns.

Although Santa María la Blanca has not been a synagogue since it was seized and turned into a church at the beginning of the 15th century, some feel the time has come for it to be returned to the Jewish community.

Isaac Querub, the president of Spain’s Federation of Jewish Communities, is calling on the archbishop of Toledo to demonstrate the church’s commitment to interfaith relations through the symbolic gesture of handing back the building.

More than five centuries after Ferdinand and Isabella ordered Spain’s Jews to convert or leave the country – and 42 years after Pope Paul VI repudiated antisemitism and called for “mutual understanding and respect” between Roman Catholics and Jews – Querub claims the Spanish church is lagging behind society when it comes to atoning for the mistakes of the past.

Tile showing the magen David at Santa María gift shop. Photograph: Alamy Stock Photo

“The winds of Rome have blown very weakly in Spain,” he said. “The gestures of John XXIII, Paul VI, John Paul II, Benedict XVI and Pope Francis seem to be reaching Spain very late – or not at all.”

He pointed to the Spanish government’s recent decision to introduce a law offering citizenship to the descendants of Sephardic Jews expelled in 1492, arguing that Spain had taken “giant steps” towards dealing with the sins of its past.

But he said: “Why won’t the Catholic church in Spain do the same? When someone sincerely recognises that they’ve made an error and tries to fix an injustice, they become a better person. It’s the same thing: Spain is a better place and its society has made progress. No political party opposed the law. Frankly, it was just extremely positive. The same thing needs to happen with the church: there needs to be Judeo-Christian dialogue.”

It’s not about starting a war … we want to deepen the Judeo-Christian dialogue Isaac Querub

Querub says he wrote to the archbishop of Toledo, Braulio Rodríguez Plaza, last year to request a meeting on the issue but is still awaiting an answer.

And the archdiocese of Toledo shows few signs of contemplating any return of the building. In a three-page statement, it said the church’s ownership of the now-deconsecrated building was “perfectly clear” and that the government had restored Santa María la Blanca to the care of the archdiocese through a local parish in 1929.

It said that the archbishop had met Querub twice – most recently in November last year – adding: “They agreed to meet again after Christmas, but neither Mr Querub nor anyone acting on his behalf has asked in writing for an official meeting, which is why the archbishop has been unable to respond to his request.”

The statement also pointed out that the proceeds from the museum went on the upkeep of other buildings in the archdiocese and that the archbishop had spent almost €800,000 (£685,000) on conserving the building since 2013.

It concluded with a reminder that the nearby Sinagoga del Tránsito belonged to the government, rather then the church.

The archbishop of Madrid, Cardinal Carlos Osoro Sierra, recently struck a more conciliatory note and emphasised the need for dialogue. “Gestures that bring us together and help us all are good,” he told El País. “Of course I think they’re good. Santa María la Blanca needs to be a meeting place.”

However, a spokesman for the archdiocese of Madrid told the Guardian that the cardinal had been talking in general terms and had not offered an opinion on whether the building ought to be handed back.

Visitors view horseshoe arches and wall carvings at Santa María la Blanca. Photograph: Alamy Stock Photo

Spain’s Jewish population numbers fewer than 100,000, most of whom live in Madrid, Barcelona and Málaga. There was, Querub said, no Jewish community in Toledo today but that was not the point; the federation was not looking to reclaim Santa María la Blanca as a place of worship but to use it as museum that finally acknowledges its roots and uses its original name.

“It’s not about starting a war … we want to deepen the Judeo-Christian dialogue,” he said. “We want to see action and better education: we want to see the Catholic church’s teaching centres doing more to explain what happened 2,000 years ago and teaching people about the Jewish people and the link between them and the land of Israel.”

Querub pointed to the centuries of blood libel, propaganda and the antisemitic slurs that continue to exist in the Spanish language.

“People still use the word judiada [to describe acts of cruelty or extortion] and in León [during Holy Week] they talk about ‘killing some Jews’ when they mean ‘having a few drinks’.”

He believes the return of Santa María la Blanca would be a landmark event that would demonstrate the church’s commitment to drawing a line under the past.

“But we’re not the ones who should be telling the Catholic church what it needs to do, how it needs to do it or when it needs to do it. We’d just like this symbolic gesture.”