Vienna district court said that Firtash, a backer of ousted president Viktor Yanukovych arrested in Austria late Wednesday on the basis of a US arrest warrant, has "filed an appeal against the decision".
It added that it has set bail for Firtash, 48, at USD 173.9 million on the understanding that if he pays this and is released, he will not leave Austria.
"The basis for extradition proceedings by the US authorities is suspected bribery and activities in a criminal organisation," judge Andreas Hautz said in a statement.
Mogilevich is on the FBI's 10 Most Wanted Fugitives list.
He lives freely in Moscow and is believed to have close contacts to both the Russian capital's former mayor Yury Luzhkov and top figures in the Ukrainian security service.
