The demonstrators also want the government to revoke the broadcasting licences of television channels promoting violent content, and a ban on pro-government newspapers that stir tensions by targeting political dissidents.
Serbian President Aleksandar Vucic organised a rally of his own supporters on Friday in a show of force against the opposition-led protests.
Vucic initially dismissed the protests as a "political" stunt, but seemingly softened the stance towards the demonstrators.
"Those who rallied in the past couple of weeks are, for the most part, good, decent and normal people who want what's good for Serbia," Vucic said during a rally on Friday.