Russia was outraged that ABC had felt it acceptable to broadcast such an interview and accused Washington, and the West in general, of double standards when it came to fighting international terrorism.
Moscow said the interview allowed a self-confessed terrorist and murderer to openly threaten Russia and publicise and even glorify terrorism.
"The fact that such an authoritative national channel has acted as a mouthpiece for a person who is accused of, and who in fact admits that he has tried to achieve his own ends in such a way, by seizing hostages and peaceful people, is very sad and causes deep regret," Dmitri Kozak, President Vladimir Putin's point man on Chechnya, said.
Basayev, who has a £5.7m bounty on his head, admits that he masterminded just about every terrorist attack on Russia in the last decade, including the Beslan school siege, the Dubrovka theatre siege, the Budennovsk hospital siege and last year's suicide bombing of two passenger airliners.
America's most senior diplomat in Moscow was summoned to the Russian Foreign Ministry for a dressing down, while MPs called on the Kremlin to retaliate against Washington through diplomatic channels. Russia's ambassador to the United States apparently tried in vain to block the interview's broadcast and Moscow appeared to blame the American government yesterday for not doing more to stop ABC.
The fact that a Russian journalist - in this case a Radio Liberty correspondent, Andrey Babitsky - can meet Basayev, allegedly in Chechnya, is also highly embarrassing for Russia's FSB security service and armed forces who have been hunting him for years.
Babitsky said Basayev and his men lived in harsh conditions eating mainly "instant soups and canned food" and slept outdoors on the forest floor. A lean-looking Basayev admitted he was no angel. "I admit I'm a bad guy, a bandit and a terrorist ... but what would you call them?" he said of the Russians. "If they are keepers of constitutional order and anti-terrorism fighters then I spit on all those agreements and nice words.
"The Chechen people are dearer to me than the rest of the world," Basayev said, warning he had no intention of giving up. "I'm making new plans. We're always looking for new ways."
Asked whether Russia should brace itself for more Beslan-style attacks, he answered: "Of course ... As long as the genocide of the Chechen nation continues ... anything can happen."
Most controversially, he attempted to take the moral high ground when it came to the Beslan siege, in which 180 children were killed. "In Chechnya and in other places I use adequate and acceptable methods," he claimed. "Neither I nor my mujahedin have killed children. Children are not guilty. The whole Russian people is guilty. "And if the war does not come to every one of them personally the conflict in Chechnya will never end."
Taus Djabrailov, a leading pro-Moscow Chechen politician, said yesterday that the ABC interview was proof that the West had not learnt its lesson about terrorism: "(It seems that) even the tragic events on the London Underground have not prompted the West to realise what a threat people like Basayev pose to the whole world."