Mukhtar Ablyazov is accused of stealing billions of dollars from the Kazakh BTA Bank, which also operates in Russia and Ukraine.
The court said Russia should take priority.
Mukhtar Ablyazov was arrested on the French Riviera last July.
He denies the allegations. His children say his life would be in danger if he were to be transferred to Kazakhstan.
Both Ukraine and Russia have requested his extradition.
Mukhtar Ablyazov’s lawyer said he would appeal against the ruling.
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