Russia insists that it is not going to talk to Mr Maskhadov, because he does not "control the situation" in the republic - a claim the Chechen president rejects.
Though he is ethnically Chechen, Anzor Tsarnaev grew up in the former Soviet republic of Kyrgyzstan because his parents were deported there in the Stalin era alongside many other ethnic Chechens.
The ethnic Chechen family came to this country in 2002, after fleeing troubles in Kyrgyzstan and then Dagestan, a predominantly Muslim republic in Russia's North Caucasus.