Croatia's presidential election will go to a run-off after no candidate polled more than 50% in Sunday's election.
Mr Mesic just failed to gain outright victory
Incumbent President Stipe Mesic, who attracted 49% of the vote, will face Deputy Prime Minister Jadranka Kosor in the second round on 16 January.
But Mr Mesic remains the favourite. Ms Kosor received just over 20% of votes.
Political observers believe the low turnout in the election - just over 50% - may have contributed to Mr Mesic failing to win in the first round.
The fact that there were 13 candidates disputing the election may also have contributed.
One of them, the wealthy US-based businessman Boris Miksic, attracted significant support at nearly 18%.
On hearing the results, based on 99% of polling stations reporting, Mr Mesic declared it a "brilliant victory" and declared confidence that he would win a second five-year term in office, according to AP news agency.
Ms Kosor said she was "sure Croatia is mature enough to finally have a female president".
The campaign has been dominated by the prospect of Croatia's potential European Union membership, and the handover of suspects to the war crimes tribunal in The Hague.
Ms Kosor says Croatia is ready for a woman president
The extradition to The Hague of the fugitive general, Ante Gotovina, is seen as a key condition for Croatia to start membership talks with the EU.
Both Mr Mesic and Ms Kosor favour co-operation with The Hague and the goal of EU entry - the issue above all others likely to dominate the term of office of whoever is elected as Croatia's next president, says the BBC's Nick Hawton in Sarajevo.
He says much now depends on how the defeated presidential candidates tell their supporters to vote, particularly Mr Miksic.
The powers of the Croatian president are limited, and most decisions are made by the prime minister and parliament.
Mr Mesic is credited with overseeing the reduction of presidential powers as Croatia has increased its democratic credibility since the death of autocratic leader Franjo Tudjman in 1999.