Serbian Prime Minister Aleksandar Vucic has declared a "historic triumph" for his center-right Serbian Progressive Party in early parliamentary elections, promising to keep the country on its course to join the European Union.

"Serbia will continue on its European path and we'll try to accelerate it," Vucic told supporters gathered at party headquarters in Belgrade late on April 24, hours after polls closed. "There is no compromising with that."

However, he stressed that Belgrade will also maintain its friendship with Russia, its traditional Orthodox ally and supporter.

An initial projection by the independent CeSID monitoring agency said Vucic's party is set to win 49 percent of votes cast in the election.

The left-leaning Socialist Party of Serbia was set to remain the second-biggest party in parliament with 12.9 percent, while the ultranationalist Radical Party of Vojislav Seselj, acquitted last month of war crimes by a UN tribunal in The Hague, is set to be the third-largest party in parliament with 7.4 percent of the vote, CeSID projected.

The polling firm based its projections on the actual vote count at representative polling stations. The first official results are expected later this week.

Seselj, whose core ideology is based on the goal of creating a Greater Serbia, has himself publicly burned EU and NATO flags. He has also campaigned for closer ties with Russia rather than the EU, saying that would help Serbia overcome its "economic misery."

WATCH: Serbian Prime Minister Aleksandar Vucic and other political leaders marked their ballots in parliamentary elections on April 24.

"We are not happy with the election results. We expected more," Seselj said late on April 24, adding that the Radicals would "show we are superior" in parliament.

Following a sluggish start, the pace of voting picked up in the April 24 election, with total turnout expected to surpass the 53 percent threshold registered in Serbia's 2012 parliamentary elections.

Vucic called the vote two years ahead of schedule, saying he needed a stronger mandate than the 131 seats that the Serbian Progressive Party now controls -- just over half the 250 seats in parliament. Such a mandate, he said, would help him achieve his stated goals of bringing Serbia closer to European Union membership and bolstering the economy by pushing through reforms required by the European Union and the International Monetary Fund (IMF).

Formerly an ultranationalist who supported the idea of a Greater Serbia, Vucic now presents himself as a pro-European reformer.

Vucic and his governing coalition partners narrowly missed securing a two-thirds majority in the 2014 vote, when they won 158 seats.

WATCH: Serbs went to the polls on April 24 in early parliamentary elections to vote members of the country’s National Assembly. More than 6.7 million registered voters were also choosing councilors in local elections. (RFE/RL’s Balkan Service)

Formed by the late Slobodan Milosevic and led by Foreign Minister Ivica Dacic, the Socialists before the April 24 vote were in control of 25 seats. The party has opposed the large-scale privatization of loss-generating state firms called for by Brussels as a condition of closer EU integration, and that the IMF has made a condition of a 1.2 billion-euro ($1.35 billion) loan.

In fact, the Socialists' opposition to privatization deals caused tension with Vucic, who has said he needs a good review in May from the IMF on Belgrade's reforms or it would be "very difficult" for him "to be the prime minister."

The Social Democratic Party of Serbia, led by ethnic Bosniak politician and Trade Minister Rasim Ljajic, rounded out the governing coalition before the April 24 ballot with nine seats in the National Assembly.

The Social Democrats are a part of the Alliance For a Better Serbia -- a coalition that also includes the Liberal Democratic Party of Serbia and the League of Social Democrats of Vojvodina.

Vucic, a former Seselj ally, said as he cast his ballot in a rainy Belgrade suburb that he "not going to make any compromise" with right-wing parties.

The head of Serbia's Government Office of Kosovo, Marko Djuric, said that polling stations will be open in Serb-inhabited areas of Kosovo.

More than 110 countries recognize the independence of mostly ethnic Albanian Kosovo, but Belgrade insists it remains a province of Serbia.

Kosovo's constitution allows for dual citizenship for the Serbian community.

In previous Serbian elections, the government in Pristina did not allow Serbia's Election Commission to organize balloting within Kosovo. But the Organization for Security and Cooperation in Europe (OSCE) reached a deal with Pristina that will allow the organization to collect the votes of Kosovo Serbs.

The OSCE carried out a similar role in Kosovo for Serbia's 2012 and 2014 parliamentary elections.

With reporting by dpa, Reuters, AP, AFP, and B-92