Yevgeni Nikulin, sought by the US for alleged cyberattacks on social networks and also by his native Russia on fraud charges, has been in a Prague prison since he was arrested in the Czech capital in October 2016 in a joint operation with the FBI.
The case comes amid accusations by Washington that Russia tried to "interfere" through hacking in the 2016 US election won by Donald Trump, charges the Kremlin has dismissed.
Last May, a Prague court ruled that the 30-year-old Nikulin can be extradited to either Russia or the United States, with the final say left to Justice Minister Robert Pelikan.
"It's true that there have been two meetings this year at which the president (Milos Zeman) asked me to extradite a Russian citizen not to the United States, but to Russia," Pelikan told the aktualne.cz news site.
The site said the meetings had taken place in January, while earlier this week Pelikan received Vratislav Mynar, the head of Zeman's office, who also lobbied for Nikulin's extradition to Russia.
"It's none of your business, but I have handed the minister a letter from the detained Nikulin's mother," Mynar told aktualne.cz.
Zeman's spokesman Jiri Ovcacek declined to comment on the matter when asked by AFP.
Following Nikulin's arrest, Moscow accused Washington of harassing its citizens and vowed to fight Nikulin's extradition.
It then issued a separate arrest warrant for him over alleged theft from the WebMoney settlement system.
The US has charged Nikulin with hacking into social networks LinkedIn and Formspring and into the file hosting service Dropbox, Nikulin's lawyer Martin Sadilek told AFP earlier.
He also said Nikulin alleges that FBI investigators had tried twice to persuade him to confess to cyberattacks on the US Democratic Party.
Zeman, a 73-year-old ex-communist with strong pro-Russian, pro-Chinese and anti-Muslim views, won a second five-year term in a presidential vote in January.
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