Kasparov was one of several Russian opposition leaders to rally in support of the female punk band known as Pussy Riot.
Kasparov spoke Tuesday at the conservative Heritage Foundation for a conference critical of the reset with Russia.
“The utmost task for the opposition is how to offer a vision for the future,” Kasparov said.
For Kasparov, he sees similarities between Ilyumzhinov and Putin.
Kasparov is the chairman of the United Civil Front in Russia and a global voice for human rights.
Since news of his arrest, Kasparov said he had received warm messages of solidarity from his friends and supporters.
Since 2005 Kasparov has been an important leader for the coalition of groups opposing Putin and his party, United Russia.
Kasparov said when he was in the van, the police officers continued to beat him.
For Kasparov, his arrest and the trial of Pussy Riot “just shows that Russia has nothing to do with the rule of law.”
Kasparov said he went to the trial to show his support for Pussy Riot.