Mr. Putin announced the move Thursday during a meeting with Alkhanov.
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The Russian leader appointed Chechnya's Prime Minister Ramzan Kadyrov to replace Alkhanov. Kadyrov is the son of the late Chechen president Akhmad Kadyrov, who was assassinated in 2004.
President Putin appointed Alkhanov as deputy justice minister of the Russian federation.
Kadyrov has denied accusations that militias he controls are behind the abductions and abuse of Chechen separatists and civilians believed to have links with them.
Major fighting in Chechnya ended in 2001, but violence remains common in the mostly Muslim region.
Some information for this report was provided by AFP and AP.