The Vatican has denied a claim by the Spanish government that the church would cooperate to ensure the remains of Gen Francisco Franco are not reburied in Madrid’s Almudena Cathedral after exhumation from the dictator’s famous mausoleum.

The socialist government of Pedro Sánchez has committed itself to removing Franco’s body from the Valley of the Fallen outside the Spanish capital, arguing the move would close wounds “that have been open for many years”.

But Franco’s family has dismissed the initiative as a political stunt, saying that if the dictator were exhumed, his remains ought to be interred in the family vault in the Almudena cathedral.

The government is deeply opposed to a reburial in the cathedral as it could turn it into a pilgrimage site for the far right.

On Monday, Spain’s deputy prime minister, Carmen Calvo, travelled to the Vatican to broach the exhumation issue with the Vatican’s secretary of state, Cardinal Pietro Parolin.

Calvo gave details of the meeting on Tuesday, saying: “We’ve agreed, with the Catholic church, to work together to find a solution that obviously can’t be the Almudena [Cathedral].”

She said the government would not allow Franco’s remains to be venerated or celebrated, adding that it possessed the necessary legal tools to stop that happening.

“The cardinal appreciated that we have to find a solution so that while Franco’s remains are laid to rest with dignity, they are not the object of any kind of homage,” she said.

However, the director of the Vatican press office, Greg Burke, issued a statement later on Tuesday, denying that an agreement had been reached to prevent Franco’s body being reburied in the cathedral.

“With regard to the meeting yesterday between the secretary of state for the Holy See and the deputy prime minister of Spain, I would like to make the following point clear: Cardinal Pietro Parolin is not opposed to the exhumation of Francisco Franco – as decided by the relevant authorities – but he did not at any point express a view as to the place of reburial,” said Burke.

“It’s true that Mrs Carmen Calvo expressed concern over the possible burial in the Almudena Cathedral and her desire to explore other alternatives – including through dialogue with the [Franco] family. The secretary of state suggested that would be appropriate.”

Calvo’s remarks went further than an official Spanish government statement released on Monday afternoon, which said that Parolin had offered a guarantee that the Vatican would not oppose the exhumation, and which stressed the importance of dialogue and finding a solution.

News of the apparent deal also came as a surprise to the archbishop of Madrid’s office. Sources there told the online newspaper eldiario.es that they did not want to be used “as a political football” and were not familiar with the details of the talks between Calvo and Parolin.

They also renewed their calls for dialogue between the government and the Franco family to resolve the issue. While the government can exhume Franco’s body, it will be up to the family to decided where it is reburied.

The most likely alternative – should the family give its consent – would be to bury the dictator in the El Pardo cemetery on the outskirts of Madrid, where his wife’s remains are interred.

Forty-three years after Franco died, his final resting place remains a controversial and divisive issue. Thousands of people gathered outside the Almudena Cathedral on last week to protest against his possible burial there.

The Valley of the Fallen, which was partly built by captured republicans and political prisoners, is a mass grave containing the remains of more than 30,000 people who fought on both sides of the Spanish civil war.

However, only two graves are marked: Franco’s and that of José Antonio Primo de Rivera, the founder of the Falangist party.