The crowd waved flags and sang nationalist songs within earshot of their Albanian neighbours.
Nikolic has had a slight lead in recent opinion polls and has vowed to strongly fight Kosovan independence.
He said: "Serbia will never accept the independence of Kosovo. We must never give up or give in."
The result of the presidential contest is set to have a major influence on how Serbia responds to any Kosovan declaration.
Tadic and Hashim Thaci, Kosovo's prime minister, are attending a UN security council meeting in New York on Wednesday.
Despite the imminent declaration of independence, officials claim the meeting will cover the current operations of UN mission in Kosovo (UNMIK).
Libya's Giadalla Ettalhi, the security council president, said Tadic would be allowed to speak in an open debate but that Thaci, a former ethnic Albanian Kosovan resistance leader, would speak in a closed-door session.
John Terret, Al Jazeera's correspondent in New York, said the declaration could come as early as March.
It is likely to be approved by the United States and a number of European countries, but Serbia and its ally Russia have vowed to oppose it.
During the UN meeting, the 15-member council will hear a briefing by Joachim Rucker, UN special envoy for Kosovo, on the latest report on the activities of UNMIK.
In his report, Ban Ki-moon, the UN secretary general, warns that the status quo in Kosovo "is not likely to be sustainable."
The report states: "Should the impasse continue, events on the ground could take a momentum of their own, putting at serious risk the achievements and legacy of the United Nations in Kosovo."