Lawmakers approved a measure Tuesday that would increase the fine to a maximum of $29,000, but the RIA Novosti news agency said the highest fine was expected to be reduced to $9,600 in a second reading of the measure.
Fines for organizers failing to comply with federal regulations on demonstrations would increase from $1,160 to $48,000.
The advisory Kremlin human rights council said Wednesday it planned to ask President Vladimir Putin to veto the measure if it is approved by both houses of Parliament.
"These fines exceed the annual earnings of an average worker," said rights activist Lyudmila Alexeyeva, a member of the Kremlin human rights council.
RIA Novosti said average monthly salaries in Russia are about $900 but higher -- $1,470 -- in Moscow and St. Petersburg.
"People will still go to demonstrations though," Alekseeva said. "You can't keep dissatisfied people at home."
Deputies from the ruling United Russia party proposed the higher fines for illegal protests after clashes between police and demonstrators at a Moscow rally the day before Putin's May 7 inauguration as president.
With United Russia's majority in Parliament, the draft bill passed over objections in the State Duma from three opposition parties -- the Communists, the Liberal Democratic Party and A Just Russia Party.
Prime Minister Dmitry Medvedev, who takes over leadership of United Russia this month, has criticized the proposed higher fines.
"We need to change ourselves and not just make harsher punishments," he said last week.