The chief mufti, Ravil Gainutdin, said on 1 December that he would pull out from the council unless it condemns a recently published book that allegedly contains slanderous remarks about the country's Muslim leaders.
The ultimatum is contained in a statement posted on the website of the Russian Council of Muftis.
In the statement, Gainutdin claims the book -- called "A New History Of Russia's Muslim Community" -- "contravenes all elementary principles of ethics and morality."
The author of the book is Roman Silantev, the executive secretary of the Inter-Faith Council and a member of the Moscow Patriarchate. Silantev has said his book focuses on the "positive side" of Islam in Russia.
The Inter-Faith Council was set up in 1998 to promote dialogue among the Russia's Orthodox Christians, Muslims, Buddhists, and Jews.