He now faces Jadranka Kosor of the governing Croatian Democratic Community in a 16 January runoff. Kosor finished second among 13 presidential candidates with about 20 percent.
Mesic had predicted that the election would go to a second round. And the mood at his campaign headquarters in Zagreb was jovial shortly after midnight today when the results were announced.
"I would like to thank all those who gave me their vote. It means that they recognize Croatia is on the right track and that we are aiming to achieve the standards of the developed world. This is what we stand for," Mesic said.
Analysts in Zagreb say Croatia will benefit from having two pro-Western candidates in the runoff, as the winner will preside over Croatia's drive to join the EU by 2009.
The post of president is largely ceremonial, although it does have influence on foreign, defense, and intelligence policies. Moreover, some analysts suggest a Mesic victory could further solidify Croatia's turn away from the hard-line nationalism once associated with the HDZ of late President Franjo Tudjman.
Both Mesic and Kosor say they support joining the EU. Today, Mesic insisted he is the best candidate to ensure that Zagreb joins the bloc on schedule in 2009. "In the next round [of the presidential election], we are deciding where Croatia is going -- whether it will move into the 21st century or turn back," Mesic said. "I am offering the 21st century and a modern, decent, independent Croatia."
Kosor told journalists today that she is determined to put the needs of the Croatian people above politics and to protect national interests as Croatia moves toward the EU. "I have a message -- that people are more important than politics for me," kosor said. "I think I have already proven that. And the second message is that if I win [the second round ballot], I will be a strong and fair president for all those who always protects Croatia's national interests."
But few analysts in Zagreb believe Kosor will win the second-round vote.
Analyst Tomislav Jakic, who formerly served as a foreign-policy adviser to Mesic, told RFE/RL: "I agree with those who think that in the present circumstances -- provided there are no big surprises of any kind -- President Mesic is bound to win the next round because if you take the votes gained [yesterday] by his opponents all together, they don't have as much as he won yesterday," Jakic said.
Political observers in Zagreb also are taking note of a strong third-place finish by Boris Miksic, a candidate who launched a multimillion-dollar business in the United States. Miksic picked up 17.8 percent of yesterday's vote.
Jakic told RFE/RL that the strong support for Miksic is a significant political development. "It means that the Croatian electorate is fed up with politicians they have known for years," he said. "It shows that the Croatian electorate wants not only new people, but people who at least claim they are honest. This was Miksic's slogan: 'An honest man for the president.'"
Jakic said Miksic won support from many hard-line nationalist voters while, at the same time, presenting himself as a candidate with proven abilities in international business. "Miksic was an outsider. He is still not very well known by the Croatian public. He lived in the United States for more than two decades. He was allegedly a very successful businessman there. He did play a little bit on the nationalistic tunes. He opposed, to a certain degree, future collaboration with the Hague tribunal for war crimes -- which suits the rightist voters. So his campaign was a mix of 'I am a good guy from overseas. I am an honest person,' and 'I am one of you Croatian nationalists,'" Jakic said.
Jakic expects most of Miksic's supporters to vote for Kosor in the second round. But he said that even if all of those voters cast their ballots for Kosor, it is still unlikely to be enough to defeat the incumbent.
(Mirijana Rakela of RFE/RL's South Slavic and Albanian Languages Service contributed to this report.)