"There are no illusions that what is being called elections was the most unfair and dirtiest in the whole history of modern Russia," Kasparov said at a news conference, pointing at reports of massive vote violations.
"We fully realize that it's useless to seek the truth in Russian courts," he added.
Kasparov, who heads the Other Russia coalition of opposition groups, was arrested and jailed for five days for leading a protest rally in Moscow on Nov. 24. His group was not allowed to run for parliament.
Kasparov said that activists of the pro-Kremlin youth group Nashi, which means Ours, attacked his group's office Monday.
Earlier Monday, Nashi held a rally in Moscow, mobilizing its supporters to thwart what it described as a possible attempt by U.S.-backed "thieves and traitors" to mount protests and seize public buildings and squares. A U.S. Embassy spokeswoman called the claim "ridiculous."
Near the United Nations Glass Palace in New York, there is a metallic sculpture entitled "Evil Defeated by Good", representing Saint George transfixing a dragon with his lance. It was donated by the USSR in 1990 to celebrate the INF Treaty concluded with the USA in 1987