President Vladimir Putin on Wednesday defended a bill introducing fines of $30,000 or more for people who organize or participate in unauthorized rallies.
The Kremlin human rights council had asked him to veto the bill.
Media reports have said the bill could be enacted into law before the planned large-scale opposition rally on June 12.
That rally is expected to be similar to the one broken up by police on Bolotnaya Ploshchad on May 6.
"I believe that we must … do everything possible to make this bill a democratic one," the council's head, Mikhail Fedotov, told Putin at a United Russia convention Wednesday.
"And if that doesn't happen, then the council will ask you to veto this bill," Fedotov said, Interfax
Putin seemed to agree with Fedotov, saying "any amendments … must strengthen the democratic nature of our state."
But he added that laws "must protect people from extremely radical outpourings" and "must be well-balanced," Interfax
The State Duma on Tuesday tentatively approved the bill, which would increase fines from 2,000 rubles to 1 million rubles (from $65 to $32,400).
Penalties on organizers would climb from 5,000 rubles to 1.5 million rubles.
The second reading of the bill is set for June 5, and the third reading can be held the same day, Kommersant
Meanwhile, Alexei Mayorov, head of City Hall's regional security department, told Kommersant on Wednesday that opposition protesters can return to Chistiye Prudy if they don't stay there overnight.
Protesters were forced from Chistiye Prudy on May 16 following a Basmanny District Court ruling that validated local residents' noise complaints.
Human rights organization Agora appealed the ruling. A date for a hearing on the appeal has not been set.