A Kremlin source contacted by Reuters dismissed the statement, saying he would not comment on what he described as an "idiotic" claim. Russian markets also shrugged off the news.
The letter, signed by the "Battalion of Martyrs," was posted on the kavkazcenter.com website, which claims to represent Chechen rebels.
The letter said the main Chechen rebel leader in hiding, Doku Umarov, who seeks an Islamic state in the North Caucasus, had decided to step up a campaign of economic war on Russia.