Milosevic, 64, who was on trial for war crimes, was found dead in his prison cell at the UN detention centre near The Hague.
A UN spokesman said he had died of natural causes.
Milosevic's lawyer, Zdenko Tomanovic, said: "I informed the Russian embassy on behalf of Mr Milosevic about his claims that his health was being wilfully destroyed, and that this should be (investigated) by the Russians."
Tomanovic told reporters at The Hague that he had now filed an official request to the tribunal for the autopsy to be carried out in Moscow.
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