According to the RIA-Novosti news agency on Tuesday, Airat Vakhitov said the litigation was not about money.
Formerly an imam in the Russian republic of Tatarstan, Vakhitov said: "It's not a question of compensation. I want the United States to publicly recognise my innocence."
Vakhitov, one of seven Russian nationals released from Guantanamo in February 2004, said he had already given testimony to a US civil court examining his complaint.
He said that US soldiers at Campt Delta, in Guantanamo Bay, Cuba, had tried to provoke detainees by insulting the Quran. "They threw the Quran in the toilets before our eyes," said Vakhitov, adding that this happened regularly.
Other detainees were "poisoned with gas" and guards unleashed dogs on them, he said.
In an interview published in the Russian daily Gazeta on Tuesday, Vakhitov said he left Russia in the autumn of 1999 for Tajikistan.
He was then abducted by members of the Islamic Movement of Uzbekistan, an armed group fighting to topple secular leadership in Central Asia.
Vakhitov said he was then taken to Afghanistan, where he was arrested by the country's Taliban government and detained in a prison in Kandahar in the south of the country.
He was transferred to Guantanamo after the arrival of US troops in 2001, he told Gazeta.