But he put the ultimate blame for the massacre of more than 330 people held hostage in a school on Russian President Vladimir Putin.
In a letter posted on Friday on the Kavkaz-Center website, Basayev said he had sent a letter to Putin proposing "independence (for Chechnya) in exchange for security".
It was impossible to confirm whether the letter was genuine, but the web site has posted his previous claims of responsibility.
He said that if Russia withdrew its troops, Chechnya would neither support nor finance groups fighting Russia, and "we can guarantee that all of Russia's Muslims [will] refrain from armed methods of struggle against the Russian Federation, at least for 10-15 years, on condition that freedom of religion as is guaranteed in the Russian Federation be respected".
"We can guarantee that all of Russia's Muslims will refrain from armed struggle ... on condition that freedom of religion as is guaranteed in the Russian Federation be respected"
Shamil Basayev, Chechen independence leader
Basayev said his band was responsible for an August explosion at a bus stop outside Moscow, the near-simultaneous bombings of two planes the same night, a bombing outside a Moscow subway station a week later, and the school hostage-taking that ended in a hail of gunfire and explosions. More than 430 people have been killed in the attacks.
"A terrible tragedy occurred in the city of Beslan; the Kremlin vampire destroyed and wounded 1,000 children and adults, giving the order to storm the school for the sake of imperial ambitions and the preservation of his own throne," Basayev wrote.