Spain’s deputy prime minister will travel to the Vatican on Monday amid speculation that the government could use the visit to try to enlist the Roman Catholic church’s help as it seeks to exhume and reinter the remains of Gen Francisco Franco.

The socialist government of the prime minister, Pedro Sánchez, has committed itself to removing Franco’s body from the Valley of the Fallen, the huge mausoleum outside Madrid where the dictator has lain since his death in 1975.

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 war.

The Valley of the Fallen, where Gen Franco is buried. Photograph: Óscar del Pozo/AFP/Getty Images

While ostensibly a monument to all those killed in the conflict, only two graves are marked: Franco’s and that of José Antonio Primo de Rivera, the founder of the Falangist party.

Sánchez said the move was intended to close wounds “that have been open for many years”, but the dictator’s family has bitterly opposed the exhumation.

Although the government can have Franco’s remains moved, their place of reburial remains a matter for the dictator’s family. The most likely reinterment site is Madrid’s Almudena Cathedral, where the Franco family owns a crypt.

Protesters gather outside the Almudena cathedral to urge authorities to prevent the remains of Franco being reburied there. Photograph: Paul White/AP

The cathedral, however, sits in the centre of the capital, close to the royal palace, meaning that a reburial there would make Franco’s grave more accessible and could turn the cathedral into a pilgrimage site for the far right.

The deputy prime minister, Carmen Calvo, was asked earlier this week whether she would ask the church to step in when she meets the Vatican secretary of state, Cardinal Pietro Parolin. She said there were “many issues to discuss”.

Calvo added: “Even though [Franco] was a dictator, they are human remains and only his family can take charge of them or decide where they should go.”

She said the government had undertaken to exhume Franco to comply with both Spain’s historical memory law and with UN reports “so that Franco is not in a state tomb in a public place where he is glorified as a dictator”.

Thousands of people gathered outside the Almudena Cathedral on Thursday to protest against Franco’s possible burial there.

The Francisco Franco National Foundation, which seeks to promote the dictator’s legacy, has warned that the government’s initiative could backfire.

“If, God forbid, Franco’s remains end up in the Madrid cathedral, the pilgrimage to see him is going to be tremendous,” the foundation’s president, Juan Chicharro, told the Associated Press.

“You can only reach the Valley of the Fallen by car on a motorway and with traffic jams, but you can easily get to the cathedral on the metro.”

Gen Franco watches a parade march past in Spain in 1969. Photograph: Rolls Press/Popperfoto/Popperfoto/Getty Images

One alternative would be to persuade the Franco family to bury the dictator in the El Pardo cemetery on the outskirts of Madrid, where his wife lies.

Vatican experts say the church is unlikely to make any official intervention as the issue is one for Spanish bishops.

“This is a matter for the local hierarchy – Spaniards are divided on this but, from what I’ve seen, the local Catholic hierarchy has been pretty clear that they don’t want anything to honour Franco,” said Robert Mickens, the Rome-based editor of the English-language edition of Catholic daily newspaper La Croix.

“[With] Parolin being one of the most savvy diplomats within the Holy See, I think he’ll be very careful with how he will comment or not comment.”

Andrea Tornielli, a Vatican expert at La Stampa and the coordinator of the newspaper’s Vatican Insider website, said Franco had the same right to a tomb as anyone.

“It is clear that as long as there is an open legal process, that is, the Franco family’s rejection of the government and all its institutions, the problem is that nothing will be done, in the sense that it will take months before this problem is resolved legally,” he said.

“However, the Vatican has nothing to do with it.”