Paya died Sunday near Bayamo when the car he was driving "lost control and smashed against a tree, according to eyewitnesses," a foreign ministry spokesman told Spanish news agency EFE. Fellow dissident Harold Cepero was killed in the accident and the status of one other man in the vehicle was not reported.
Paya's daughter, Rosa Maria Paya, told CNN she doesn't believe her father's death was an accident.
"There was a car trying to take them off the road, crashing into them at every moment. So we think it's not an accident,'' she said. "They wanted to do harm and they ended up killing my father."
Paya was best known for his role in organizing the Varela Project, a gathering of signatures on a petition in support of laws guaranteeing freedom of speech and other civil rights, the Miami Herald reported Monday.
"He was a unique human being. His killing, there is no other way of explaining it, is a major setback for those who would like to see democracy and human rights in Cuba. But I'm sure the Cuban people will overcome the feeling of pain that we suffer and continue to work for what he worked for all his life," said Frank Calzon, director of the Center for a Free Cuba.