In an interview published by the Swedish TT news agency on Monday, Basayev said he was no longer bound by a commitment to peace he had given former Chechen leader Maskhadov.
Russian security forces killed Maskhadov on 8 March.
"Nobody can prevent me from responding to violence with violence," TT quoted Basayev as saying in written replies to questions the agency said it had submitted by e-mail.
Basayev has been blamed by Moscow for a series of bloody strikes against civilian targets including last September's Beslan school massacre.
Moscow has promised a $10 million reward for Basayev.
The Chechen separatist said he spent 12 days with Maskhadov in November and told him he would not derail negotiations to end the war, adding that Moscow had secretly offered talks.
"Maskhadov was killed as a result of the Russians' deviousness, because of his exaggerated peace efforts and I am now released from my commitments," he added.
Russia started the decade-old conflict in Chechnya, he said, adding that the Kremlin held the keys to peace.
"Maskhadov was killed as a result of the Russians' deviousness, because of his exaggerated peace efforts and I am now released from my commitments"
"We fight only against Russia and so far only on its territory. You can expect acts of sabotage, not acts of terror, only in Russia and Qatar," he said, referring to the Gulf Arab state where exiled Chechen separatist leader Zelimkhan Yandarbiyev was killed last year.
He said Russian President Vladimir Putin's remarks about bin Ladin being Basayev's commander had made him want to meet the mastermind of the 11 September 2001 attacks on the United States.
"I know one thing, he cannot be a bad man because in all the pictures I have seen of him his face radiates a strong light," said Basayev.