Opinion polls suggest there is little to call between incumbent Tassos Papadopoulos and his two main challengers, Demetris Christofias and Ioannis Kassoulides.
All three claim to be the best person to lead negotiations with the north of the island. Cyprus has been divided since a Turkish invasion in 1974 following a brief Greek-Cypriot coup.
If no winner is declared, a second round of voting will take place on February 24.
"The future is in our hands. I hope that with the help of the people we can achieve the solution we want and deserve," Papadopoulos, 74, said on Sunday.
The incumbent president, who is expected to be marginally in front at the close of Sunday's vote, was the driving force behind Greek Cypriot opposition to a UN reunification plan in 2004. The plan was accepted by Turkish Cypriots, yet Papadopoulos has said he would again oppose efforts to resurrect the plan.
Kassoulides and Christofias have said that they will try to improve ties with Turkish Cypriots.
"Our aspiration is to reunite this country and its people, Greek and Turkish Cypriots," said Christofias, 62, leader of the Communist party.
Kassoulides, 59, is in favor of moving Cyprus closer to Europe.
The failure of the international community to recognize Northern Cyprus was highlighted by Russian President Vladimir Putin last week during his final annual question and answer session as president.
Referring to Western plans to recognize a unilateral declaration of independence of Serbia's breakaway province of Kosovo, Putin said, "I don't want to offend anyone, but Northern Cyprus has been a de facto independent republic for 40 years. Why then don't you recognize it? Aren't you, Europeans, ashamed of applying double standards in solving identical problems in different parts of the world?"