Federal Security Service head Nikolai Patrushev told President Vladimir Putin that Basayev had been killed overnight in a special operation conducted by Russian forces in Ingushetia, the area of southern Russia that borders Chechnya. Patrushev's meeting with Putin was shown on Russian state television.
Basayev, 41, was behind some of Russia's worst terror attacks, including the seizure of a Moscow theater in 2002 in which dozens of hostages and militants died, the 2004 school hostage taking in Beslan that killed 331, and the seizure of about 1,000 hostages at a hospital in Budyonnovsk that killed about 100.
Basayev wasn't in Beslan for the attack, but claimed to have organized both of the operations, CBS News correspondent Elizabeth Palmer reports.
Basayev was so wanted for these attacks that Russians announced his death half a dozen times over the years, Palmer reports. For Putin, eliminating Basayev — a fundamentalist Muslim — had become a personal crusade.
"This is the retaliation he deserved for killing our children," Putin said.
Patrushev gave no details of Basayev's death in his televised remarks, but an Ingush regional Interior Ministry official, speaking on condition of anonymity because he was not authorized to speak to the media, said he had been killed while accompanying a truck filled with 220 pounds of dynamite that blew up in the Ingush village of Ekazhevo early Monday.
Basayev was among four militants killed in the blast.
The Kavkaz-Center Web site, which is considered a voice for Basayev, confirmed that he died "as a martyr." Citing a member of the rebel parliament, Abu Umar, it said Basayev had died in an accidental explosion of a truck Monday.
"There was no special operation. Shamil and other brothers of ours became martyrs by the will of Allah," he said. The site confirmed three other rebels had been killed in the blast.
The Interfax news agency quoted Ingush Deputy Prime Minister Bashir Aushev as saying that Basayev's body had been identified "through some of the fragments, including his head."
Patrushev told Putin that the Chechen rebels had hoped to "put political pressure on the Russian leadership" during the Group of Eight summit later this week, which Putin is chairing.
Patrushev said the operation to eliminate Basayev, in which many other rebels were killed, was thanks to intelligence operations abroad, "especially in those countries where arms were collected."
"This is deserved retribution for our children in Beslan, for Budyonnovsk, for all the terrorist attacks that they committed in Moscow and in other regions of the Russian Federation including Ingushetia and the Chechen Republic," Putin said, adding that everyone who took part in the operation should be presented with state medals.
President Bush said the man believed responsible for Russia's worst terrorist attacks in recent years had it coming. Asked about Basayev's death, Mr. Bush said, "If he's in fact the person who ordered the killing of children in Beslan, he deserved it."