The Russian Foreign Ministry summoned a senior U.S. diplomat in Moscow to express its "strong indignation over the Thursday broadcast," the BBC reported.
During the "Nightline" interview, Basayev admitted taking part in the 2004 raid on a school in Beslan, but said the Russians were also terrorists.
Basayev, Russia's most wanted man, also warned of further Beslan-type attacks.
More than 340 people were killed, at least 172 of them children, when Russian security forces stormed hostage-takers at a school in Beslan, North Ossetia, on Sec. 3, 2004.