Borovkov said the charge was linked to interviews Berezovsky granted to the Guardian newspaper, Echo of Moscow radio station and Agence France-Presse, in which the oligarch appeared to call for a violent overthrow of power in Russia.
British authorities, who granted Berezovsky political asylum in 2003, condemned the remarks made in the Guardian interview in April, saying the oligarch should respect Britain's laws.
Berezovsky, once a key Kremlin figure, is already wanted on fraud charges and faces a separate trial in absentia for embezzling and laundering funds from Russian airline Aeroflot.
Russia continues to struggle for Berezovsky's extradition from Britain.
The trial is due to start on July 12, Borovkov said, adding that the oligarch's lawyers refused to take part in preliminary hearings on Monday and that a defence lawyer was therefore appointed by the court.
Berezovsky built up his fortune with controversial privatisation deals in the 1990s and was seen as a key Kremlin insider who helped to engineer Vladimir Putin's rise to power before dramatically falling out with the new president.