"This vote is the first half of the match," Tadic said after casting his ballot.
"The second half, on February 3, will be a chance to once again decide to conquer Europe, a better life, better salaries and pensions, greater security."
Tadic defeated Nikolic in a run-off in 2004 after his rival topped the poll in the first round.
The incumbent president advocates integration into the European Union while Nikolic believes that Serbia should remain close to Russia, which has backed it over Kosovo, and says he favours a neutral stance between East and West.
Nikolic was an ally of Milosevic and has played on the growing frustration over US and EU backing for Kosovo's independence after the failure of almost two years of negotiations between Belgrade and Pristina over its future status.
"We do not want to argue with the European Union," he said on Sunday. "We need the EU, but not at any price."