The terrorists were on their way to carry out a major terrorist attack in Russia's North Caucasus republic of Ingushetia but they blew themselves up by accident, the Federal Security Service said.
"A truck with explosives, weapons and militants exploded, and four militants were killed," the service said.
"One of the militants in the truck has been identified as Tarkhan Ganizhev, a close associate of warlord Doku Umarov," the representative said, adding that the other three militants remained to be identified.
Umarov, 42, a successor to slain separatist leader Aslan Maskhadov, has claimed responsibility for a string of bloody attacks in Russia, including an armed raid on Ingushetia in June 2004 in which police said militants attacked 19 police precincts and prisons in the North Caucasus republic.
The security official said Ganizhev had a nickname of Tarella and coordinated several gangs operating in Ingushetia. Like Umarov, he helped carry out the 2004 attack on Ingushetia, and was also involved in the kidnapping of Ingush President Murat Zyazikov's father-in-law.
The security service said he had been wanted on several charges, including banditry and hostage taking, and added that the truck had been escorted by three cars.
"The explosion was so powerful that only some fragments of the truck were left intact," he said.
