Mikhail Filiponenko, a legislator in a Russia-installed local assembly, had been active in Luhansk's pro-Russian separatist movement since 2014.
He had served as one of the top commanders in the army of the so-called Luhansk People's Republic.
The agency said Filiponenko was eliminated in an early morning explosion.Â
He died at the site, it added on Telegram messenger.
It accused him of organising dungeons for civilians and prisoners of war in Luhansk region.
"Filiponenko himself brutally tortured people," agency said, giving no details.
The spy agency published the address at which it claimed Filiponenko lived and warned that it knew "all addresses of traitors" living in the occupied territories.
In September, Filiponenko was elected to the regional parliament in a vote that drew widespread international condemnation.
Bomb blasts targeting senior Russian-installed officials in occupied parts of Ukraine have been a regular occurrence since Russia ordered tens of thousands of troops into Ukraine in February 2022.
Luhansk is one of four Ukrainian regions Russia claimed to have annexed in September last year, despite not exerting full military control over them.
with EFE