The "Democratic Party will be at the core of the future government," party official Dragan Sutanovac said.
Nikolic, a somber former cemetery manager, predicted he will win the runoff.
"The victory is within reach," Nikolic said. "We will have a new government and a new president."
The general elections represented a sharp choice between the Democrats or nationalists, who were trying to come back to power for the first time since their former Balkan strongman ally Slobodan Milosevic was ousted in 2000.
The election for president, Parliament, and local authorities could affect the pace of Serbia's EU-demanded economic and social reforms. The country faced international isolation under Milosevic in the 1990s for his warmongering policies.
The result also could affect Serbia's reconciliation with its neighbors and wartime foes, including the former province of Kosovo, which declared independence in 2008.
The two leading election contenders were Tadic and Milosevic's former ally, Nikolic, who hoped to capitalize on the EU's economic troubles, which have dimmed the bloc's allure for many Serbs. The vote came amid the country's deep economic crisis - including a 24 percent unemployment rate - and huge public discontent with plummeting living standards.
Tadic said if he and his Democrats win, they will quickly form a new government.
"I expect that Serbia will continue on its reform path," Tadic, 54, a former psychology professor, said after casting his ballot. "Better life, better living standards for ordinary people is our strategic goal."
Nikolic claims to have shifted from being staunchly anti-Western to pro-EU. But that is not taken at face value by many Serbs and Western officials because the former far-right politician only a few years ago stated that he would rather see Serbia become a Russian province than an EU member.
Tadic, considered a moderate, advocates quick EU entry, while Nikolic, who had Russian support, said he wants to see Serbia "both in the West and East."