He and Swedish politician Jens Aron Modig survived but Mr Paya and fellow Cuban activist Harold Cepero died.
BBC: Cuba prosecutors seek seven years for Spain's Carromero
By mid-day, at Raja Ram Tiwari's Khoya Paya Shivir (Lost and Found Camp), some 4, 300 lost people have turned up.
Mr Paya's family have questioned the circumstances of the crash, alleging that the vehicle may have been forced off the road.
BBC: Cuba prosecutors seek seven years for Spain's Carromero
Mr Paya's family dispute the circumstances around the 60-year-old's death and have alleged the vehicle was deliberately forced off the road.
Paya and passenger Harold Capero died in the accident, the statement said.
Memorial services were being planned for Paya in Havana, Miami and Madrid.
Cuban prosecutors are reported to be seeking a seven-year jail term for Spanish politician Angel Carromero over the death of dissident Oswaldo Paya in a car crash.
BBC: Cuba prosecutors seek seven years for Spain's Carromero
But Mr Paya always made a point of his independence.
BBC: Cuba car crash fallout turns focus on dissidents' funds
On Sunday, Paya's daughter, Rosa Maria Paya, told CNN that her family believed a second car had struck the vehicle her father was traveling in, forcing it off the road.
The government statement says there was not a second car involved in the crash and said the rental car that Paya was traveling in lost control and crashed into a tree.
Mr Carromero has been in police custody since 22 July when a car he was driving hit a tree and crashed, killing two passengers - Mr Paya and another Cuban activist, Harold Cepero.
On Paya's website, his daughter Rosa Maria posted an audio clip saying his family believed that a second car had been involved and that it had intentionally struck the car in which Paya was traveling.
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