Spain's government is aiding a cover-up of the mysterious death of one of Cuba's most respected opposition leaders, Oswaldo Payá, who died after the car he was travelling in was rammed by an unmarked police car, according to his daughter.

Rosa María Payá accuses Mariano Rajoy's government of putting pressure on the young Spanish politician who was driving the car to remain silent about what she claims was probably murder.

The politician – Angel Carromero of Rajoy's conservative People's party – recently returned to Spain. He is now serving out the rest of a four-year jail term handed down to him in Cuba for allegedly causing the death of Payá and fellow passenger Harold Cepero through reckless driving on 22 July last year.

A Cuban court declared that no other vehicle was involved in the accident and that Carromero, who was also accompanied by the Swedish Christian democrat youth leader Aron Modrig, had been driving too fast.

But Rosa María says Payá was killed after a government vehicle hit Carromero's car first, and wants to know why the two foreigners were taken to hospital and survived while her father, who received regular death threats, and fellow anti-Castro activist Cepero died.

"There is a lot of pressure on him not to talk from his own government," she told the Guardian after meeting Carromero in Madrid last week.

Spanish government officials denied the 27-year-old politician was being put under pressure and said that he had recognised the Cuban court process as valid.

But Carromero broke his silence this week, telling the Washington Post that he had been bullied into signing a confession that he was responsible for the accident and that no other car was involved. He said the car that the four men were travelling in had been trailed by several vehicles during the day. A new car bearing official number plates had just taken over and began harassing them and driving very close when he felt a bump in the back of his hire car and spun off the road.

"The last time I looked in the mirror, I realised that the car had gotten too close – and suddenly I felt a thunderous impact from behind," he said.

He lost control of the car and then passed out, waking up in the back of a van before blacking out again and coming around on a hospital stretcher.

"The first person who talked to me was a uniformed officer of the ministry of the interior," he said. "I told her a car had hit our vehicle from behind, causing me to lose control."

He said he stuck to his story over the following days until Cuban authorities started threatening him.

"They warned me that I was their enemy, and that I was very young to lose my life," he said. "One of them told me that what I had told them had not happened and that I should be careful, that depending on what I said things could go very well or very badly for me.

"They gave me another statement to sign – one that in no way resembled the truth. It mentioned gravel, an embankment, a tree – I did not remember any of these things."

Rosa María Payá said that Modig – the youth leader of Sweden's Christian democrats, who form part of the country's coalition government – had also texted friends on the day of the accident to say that another car was involved.

But, like Payá, Modig has not been very forthcoming about the accident. "I only have vague recollections of the accident, because I had been asleep for part of the trip," he said while in Cuba, before publicly apologising for making "illegal" journeys to the island.

Modig's press chief has not replied to numerous requests for an interview from the Guardian over the past week.

On Wednesday Modig told a Swedish radio programme that he had met Rosa María this week and that, while he did not remember how the accident happened, he believed Carromero.

Rosa María now wants to know why her father and Cepero – whose Christian Liberation Movement was seen as a moderate alternative to the Castro-hating groups backed by Miami Cubans – died before reaching hospital, while the two foreigners survived. "It was not an accident. Their car was deliberately rammed but that did not cause the death of any of the passengers," she said. "The two foreigners were immediately removed from the scene. We do not know what happened to my father and his friend, but hours later both were dead. We want support for an international inquiry into the probable murder of my father and Harold Cepero."

Spanish foreign minister, José Manuel García-Margallo, said on Thursday that the government had "no evidence" that Carromero's story was true. "He should go to the courts," he advised.

Carromero did not answer calls to his Madrid home , where he is on day release from jail on Thursday. "As for the Spanish authorities, I can only thank them for managing to repatriate me," he told the Washington Post from Madrid. "I don't want to cause any more problems. I want to get my previous life back."