Yury Osipov, who was re-elected as Academy president on Friday, said no amendments should be made since "the Academy has never expelled anybody."
"It is important not to create silly precedents," he said in a reply to the proposal made by Vladimir Strakhov, who called for the expulsion of the oligarch.
Berezovsky, who lives in London after being granted political asylum, became a member of the Academy in 1991 and, despite being convicted of embezzling $43 million from a leading Russian bank, still receives a monthly salary of 10,000 rubles ($420), which will be increased to 25,000 rubles ($1,060) in June.
"If criminal proceedings are launched against a corresponding member of the Academy of Sciences, he must appear in court and prove the charges are mistaken. And if he fails to do so, he should be expelled," Strakhov told a general meeting of Academy members.
Twelve criminal investigations have so far been launched in Russia against Berezovsky, a one-time close associate of the late president Boris Yeltsin, and he also faces a criminal probe in Brazil.
The Kremlin has repeatedly urged Britain to extradite Berezovsky but all attempts have been rejected.
