Angel Carromero, a 27-year-old leading activist in the youth wing of Spain's ruling Popular Party (NNGG), is serving out his sentence in Spain after being convicted for manslaughter in Cuba.
Cuba's courts sentenced him to four years in jail after his car hit a tree in July 2012, killing two passengers including a leading Cuban opposition figure, Oswaldo Paya.
Both Carromero and the family of the deceased opposition leader blame Cuban intelligence services for the crash, alleging that a state security vehicle pursuing the car forced it off the road.
Carlos Paya Sardinas, brother of Oswaldo Paya, told news agency AFP that he had petitioned the Spanish government this year to pardon Carromero, saying "he is innocent".
But in a "purely informative" opinion directed at the Spanish government, which has the power to grant a pardon, Spain's National Court said: "We do not find any reason in law, impartiality or expedience to grant the pardon."
Carromero, who had accumulated a series of car driving penalties in Spain, was transferred from Cuba to a Spanish jail in December last year. A few weeks later the prisons service granted him relaxed "open conditions" meaning he does not have to remain incarcerated.