The demonstrators, who on Saturday gathered in front of parliament in central Belgrade, accuse Vucic of being autocratic.
They demand that the government allow more democracy, media freedoms and free elections.
Opposition leaders said authorities sought to prevent their supporters from coming to the capital for the rally, which was supposed to be the largest after four months of protests.
But police estimated the strength of the crowd between 7,000 and 10,000, fewer than on some of the regular protests held every Saturday since early December.
The organisers said that many were unable to make it to the capital because of cancelled buses and other obstacles.
Vucic’s conservative party members, meanwhile, barricaded themselves inside the parliament building and local city councils throughout Serbia on Saturday, claiming they wanted to prevent the forceful takeover of power by “fascists and thugs”.
Tensions have mounted all week as pro-government media and officials alleged that the opposition wanted to storm state institutions and take power by force.
The weekly anti-government protests have been largely peaceful.
Vucic, who denies accusations that he is an autocrat, said Saturday’s protest “will achieve nothing” and added that any troublemakers “will be removed” from the streets.
The anti-government protests started after masked thugs beat up an opposition politician last November.
Late Serbian leader Slobodan Milosevic was overthrown from power in 2000 after protesters stormed the parliament building in Belgrade.
Vucic was his close associate at the time. A pro-Vucic rally in Belgrade is planned for next Friday.