Islam Janibekov, 38, who had been living with his family in Istanbul for the last six years, was probably shot with a 7.62mm pistol with a silencer near his home on Tuesday evening, according to police.
The Turkish newspaper Sabah, citing police officials, said that the murder was carried out using a Groza, a silenced double-barreled pistol.
Grozas are used by Russian special forces and the Turkish authorities have not ruled out Russian involvement in the shooting.
Russian special forces are believed to have carried out operations in other countries, including in Qatar in 2004, when two Russian intelligence agents were convicted for a car bombing that killed Zelimkhan Yandarbiyev, a Chechen rebel leader who had taken refuge there.
Istanbul police have not commented on the incident, saying only that they are carrying out a detailed investigation.
Turkish Dogan News Agency reported that in September another Chechen rebel, Gadji Edilsultanov, was killed in Istanbul during a dispute over financial aid for Chechen separatists that was being collected in Turkey. The agency said similar circumstances could have led to the murder of Janibekov.
