Basayev claimed responsibility for the Beslan school attack in 2004, in which 331 people, half of them children, were killed.
FSS Director Nikolai Patrushev said Monday that Basayev was planning an attack to coincide with the G8 summit of world leaders this weekend in Russia.
Russian television showed Patrushev meeting Monday with President Vladimir Putin to tell him about the operation in Ingushetia -- a republic bordering Chechnya -- in which Basayev was killed early Monday.
Russian agents exploded a truck bomb next to several cars in which Basayev and other rebels were riding, according to the Interfax news agency, quoting Ingush Deputy Prime Minister Bashir Aushev.
"This is retaliation he deserves for killing our children in Beslan, Budennovsk, all the terrorist acts his bandits perpetrated in Moscow and other regions of Russia, including Ingushetia and the Chechen Republic," Patrushev said in an Interfax report.
A Chechen Web site quoted a rebel commander as saying Basayev's death was caused by an "accidental spontaneous explosion of a cargo vehicle with explosives," not Russian security agents.
Law enforcement officials in Ingushetia told Interfax that Basayev's body was in pieces but was identified by his head and by the fact that he had earlier lost a foot.
Twelve other Chechen rebels were killed in the operation, the officials said.
An Islamist Web site known to post messages from Chechen militants acknowledged Basayev's death with a statement titled "The martyrdom of the hero Basayev during a battle with the Russian forces."
The U.N. Security Council put Basayev on its official terrorist list last year after Washington classified him as a threat to the United States.
The Federal Security Service had stepped up the pressure on the country's most-wanted man in 2004 by announcing a $10 million reward for information leading to the "neutralization" of him and separatist former Chechen President Aslan Maskhadov.
Basayev, who was born in Chechnya in 1965, came to prominence in 1995 during the first Chechen war when, as a field commander, he led a hostage-taking raid in Budennovsk, Russia.
In the presidential election of January 1997, Maskhadov won a landslide over the more radical Basayev, swearing "to reinforce the independence of the Chechen state."
Basayev was appointed prime minister but resigned after serving six months.
Maskhadov later signed an agreement with Boris Yeltsin, then Russia's president, promising an end to 400 years of conflict between Moscow and the region.
Russia said it wanted to rebuild relations with Chechnya but still refused to recognize its claim of independence.
Maskhadov worked with Basayev until 1998, when Basayev established a network of military officers, who soon became rival warlords.
Chechen rebel forces crossed into Dagestan in 1999, and Moscow held Chechens responsible for a wave of bomb attacks across Russia.
Russia sent troops back into the republic, described Maskhadov's government as unlawful, and tried to build support for a parliament of Chechens in exile.
During fierce fighting, Maskhadov's government was removed from power and a pro-Moscow administration was set up. Maskhadov, later labeled a "terrorist" by Putin, was killed by Russian forces in March 2005.
During the rebel pullout from Grozny in January 2000, Basayev stepped on a land mine and lost his foot. But he and other rebel fighters eluded Russian capture.
He was helped by Islamist groups, including the Taliban, and was accused by Russia of organizing suicide bombings of Russian apartment blocks in September 1999.
Basayev said in a message on a rebel Web site that he was responsible for the Moscow theater siege of October 2002, in which 50 Chechen rebels held about 800 people hostage. Russian forces stormed the building using gas, killing most of the rebels and more than 100 hostages. (Full story (http://edition.cnn.com/2002/WORLD/europe/10/27/moscow.deaths/index.html))
He defended the operation, which Maskhadov's senior envoy condemned.
Basayev tendered his resignation from all posts in Maskhadov's rebel organization but continued to be involved in reconnaissance and sabotage.
In May 2004, Basayev said he was behind the killing of Chechnya's pro-Moscow leader Akhmad Kadyrov, and threatened to kill more officials, including the Russian prime minister. (Full story (http://edition.cnn.com/2004/WORLD/europe/05/09/grozy.blast/index.html/))
The explosion that killed Kadyrov also left six other people dead and nearly 60 wounded, including the top Russian military commander in Chechnya, who lost a leg.
Moderate rebels distanced themselves from the attack. But Basayev said he had ordered the killing after a ruling by an Islamic court.
He called it a "small but important victory" and said that other such operations against Russia's "collaborators" in Chechnya were in the making.