"We will be at the negotiating table for an agreement that will continue the existence of our people in this land with honour."
With the incumbent Talat securing 42.9 per cent of the vote, Al Jazeera's Laurence Lee, reporting from Nicosia, said the race was extremely close.
He said Eroglu had avoided a runoff just by a few hundred votes.
Talat favours reunification and closer ties with Europe while Eroglu for years has supported a two-state solution, which is rejected by the Greek Cypriots.
Stefanos Stefanou, a Greek Cypriot government spokesman, told state-run CyBC
TV that the election outcome was a "negative development", but that Dimitris Christofias, the Republic of Cyprus president, would press on with negotiations.
Tayyip Erdogan, the Turkish prime minister, said on Sunday that he will seek a solution to the Cyprus issue by the end of 2010.
"Turkish Cypriots must continue the talks which is something Eroglu also believes in. It is our aim to find a solution by the end of the year," he told Turkey's NTV.
The Mediterranean island split in 1974 into the internationally recognised Republic of Cyprus in the south and the Turkish-held Northern Cyprus. It happened when Turkey invaded the island after a short-lived coup backed by Greece.
Talat held 18 months of reunification talks with the Republic of Cyprus president.
The UN-brokered talks, launched in September 2008, were predicated on a federal solution, with distinct geographical zones for the Greek Cypriot and Turkish Cypriot communities.
Last month, Christofias and Talat announced important progress in the talks and vowed to reach a comprehensive settlement this year in a move that was widely seen as a bid to boost the latter's election prospects.
But the two sides remain far apart on the key issues of property and security.
The island's division is hampering Turkey's bid to join the European Union because of Ankara's refusal to recognise the Republic of Cyprus government.
The north declared itself independent unilaterally in 1983 and is recognised only by Turkey.