"Basayev and a number of militants were eliminated in Ingushetia last night," Nikolai Patrushev, the head of the Federal Security Service told reporters in Moscow Monday.
The separatist Islamist siege of a school in Beslan in the southern Russian republic of North Ossetia in September 2004 led to the deaths of 331 people, including 186 children.
Anatoly Safonov, Russia's envoy on international cooperation in the fight against terrorism and cross-border organized crime told the Interfax news agency Basayev's elimination was a strategic blow.
"The killing of Basayev is important not only from an anti-terrorist standpoint -- it is exceedingly important from the point of view of psychology, for the population of Chechnya," Safonov said. "He caused pain and suffering to a very large number of people."
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