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."
The attack on the Beslan school shocked Russia and divided the rebel movement, since civilians, including women and children, were taken hostage.
Basayev was the most notorious of the Chechen warlords, eluding Russian forces for years despite Kremlin vows to hunt him down and an offer of $10 million and plastic surgery to anyone providing information leading to his death.
His grim, decade-long record of killing both civilians and soldiers reflected fanatical determination — a ferocity Russia has said was bolstered by help from international terrorist networks such as al Qaeda. Washington declared Basayev a terrorist and a threat to the United States.
Basayev began his campaign even before the Soviet Union's demise, starting with the hijacking of an airliner in 1991, to attract interest in the separatist cause of Chechnya, a predominantly Muslim region in the Caucasus Mountains.
After Russian forces entered Chechnya in 1994, his exploits became more prominent. Basayev's forces buried a container of radioactive material in a Moscow park in 1995 — a warning of the mayhem they could inflict if they chose.
The Budyonnovsk hospital raid brought Basayev fame at home. When Russian troops pulled out in 1996 and Chechnya prepared to elect a president to lead it to de facto independence, Basayev ran for the job.
He lost to the late rebel commander Aslan Maskhadov and became his deputy. Basayev appeared at first to be trying to change from combatant to politician, trimming his flowing beard and trading his camouflage fatigues for a suit.
Alu Alkhanov, president of the Kremlin-backed government in Chechnya, said Basayev's killing likely would undermine the Chechen rebel movement irreparably.
"I consider that today can be considered the date of the logical end of the fight against illegal armed formations," he said, according to Interfax.
Anna Politkovskaya, a journalist who has frequently reported on Chechnya, agreed that Basayev's killing, if confirmed, would be a huge propaganda coup for Putin ahead of the G-8 summit.
"Basayev is a major symbol for Putin, and his elimination just before the G-8 summit is an amazing present for him," she said.
But she said that his death, just like that of Abu Musab al-Zarqawi, al Qaeda in Iraq's slain leader, would not bring an end to the conflict in Chechnya and the wider North Caucasus region, which has been fueled by boiling resentment of widespread human rights abuses against civilians.
"If you look at the situation in the North Caucasus, not just in Chechnya, the ranks of the rebel resistance are constantly being replenished," she said.
Another rebel leader, Doku Umarov, pledged last month that rebels would step up their attacks against Russian forces.
Umarov took over as Chechnya's new separatist leader last month after police killed Abdul-Khalim Sadulayev during a raid in an eastern Chechen town. Sadulayev's predecessor, Maskhadov, was killed in a police operation in March 2005.
Maskhadov was considered more open to negotiations than Basayev, who cultivated a reputation for ruthlessness.
Umarov last month named Basayev as his vice president. It was unclear whether that represented a radicalization of Umarov's faction or whether it was an attempt to rein in Basayev by Umarov, who had pledged not to continue attacks on civilians.