The group, Project Klebnikov, said the task force was needed because the chances of a thorough investigation and fair trial in Russia were slim due to police corruption and weak courts.
It said in a statement that it would "vigorously" examine the main theory of Russian prosecutors that Klebnikov was murdered on orders from Chechen gang leader Khozh-Akhmed Nukhayev.
Journalists are already gathering information on the "themes and threats" of Klebnikov's work to try to determine whether there were other motives for the murder, the statement said.
The Prosecutor General's Office announced in mid-June that it had established that Nukhayev, whom Klebnikov interviewed extensively for his 2003 book "Conversation With a Barbarian," was responsible for ordering the killing. It said the killing was carried out by members of a Chechen criminal group and that two were in custody.
Project Klebnikov's founding institutional members include Bloomberg, Vanity Fair and Forbes. It was set up on the first anniversary of Klebnikov's July 9, 2004, slaying.