The protestors, who gathered outside government offices, were mostly students but were also joined by labour union members and representatives from the police and the army.
Addressing the crowd, police union chief Veljko Mijailovic hailed the "major coalition of the army, police and the people," according to the Beta news agency. Another speaker called for new elections to be held.
Vucic won the presidential election in the first round on April 2 with a clear majority, garnering 55 percent of votes, and will take office as president in late May.
His main rival, ex-ombudsman Sasa Jankovic who came second in the vote with 16 percent, supported protests which began immediately after the election but urged participants to keep them non-violent.
On Saturday Jankovic said protestors were unhappy with the "injustice of the autocratic regime which threatens Serbia with dictatorship".
Saturday's protestors, estimated at over 10,000 by an AFP photographer, subsequently moved from outside the government offices to rally on the Serbia capital's major boulevards.
"There are lots of us!" and "Vucic the thief, you stole the elections!" they chanted.
"People are hungry while the those at the top are enjoying themselves," read one banner.
Vucic, who wants his country to join the European Union, said: "Everyone (has)the right to express their opinion. I don't have a problem with that. It's just important that everything happens absolutely democratically and calmly."
The protests have been organised since last Monday in Belgrade and several other Serbian cities.
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