Aug 24, 2007
Mr Basayev was killed in the Chechen capital, Grozny, during a gun battle with local police.
Moscow has pledged to track down and eliminate the Chechen rebel fighters, of whom it says there are now rapidly declining numbers.
Russian officials confirmed that two policemen had also been killed.
Chechnya itself is now relatively peaceful, but elsewhere across the North Caucasus, security remains poor.
Chechen officials say Rustam Basayev was asked for identification papers in Grozny, but fled into a nearby house, sparking a gun battle with police.
Two Chechen policemen are also confirmed dead.
Rustam Basayev was thought to be in his mid-30s, and a wrestler by profession.
He was a close associate of Doku Umarov, the underground president of the Chechen rebel movement, who has fought Russian forces for more than a decade.
For Russia, the elimination of figures like Rustam Basayev has considerable propaganda value.
Moscow has pledged to hunt down and, as it puts it, "liquidate" the remaining rebel fighters.
Russia has killed a number of top figures in the rebel movement.
Together with the installation of a loyal leader - Ramzan Kadyrov - this has allowed Russia to reassert overall control of Chechnya.
However, the wider security situation remains fraught.
Weaponry is easily available; the local police and security forces are acknowledged to be corrupt; and a rapidly growing population of young people has few economic opportunities.
In Ingushetia and Dagestan, two regions neighbouring Chechnya, attacks on servicemen and police remain common.
Dagestan, in particular, is said by many of its residents to be in a state of near-anarchy.
There, a mix of Islamists, gangsters and warring clans has made the territory largely ungovernable.