The protests took shape after the early May mass shootings that left 18 people dead and wounded several others.
Nine of the dead were students at a Belgrade elementary school who were gunned down by a 13-year-old pupil.
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.