The two presidents first held a private meeting and then were joined by their respective delegations.
The talks were followed by a ceremony where Mesic decorated Papoulias with a high state award for his outstanding contribution to the promotion of friendship and cooperation between Croatia and Greece.
Speaking at a joint press conference, Mesic described the meeting as friendly and open, saying that they had discussed bilateral relations, the situation in the region and international crises.
"We both confirmed our desire to build the future in this region together and to contribute through our friendly and close relationship to the new relations in Europe," Mesic said.
Mesic said that they were both pleased to note that Croatian-Greek relations had been gaining momentum as of late. He expressed hope that this high-level visit would help intensify the overall cooperation between the two countries.
Papoulias said that his talks with Mesic showed that the two countries had identical positions on all topics of common interest.
"We confirmed the common positions of Croatia and Greece that all problems should be resolved peacefully and through negotiation, and I trust that it is in our common interest that the problems in the region should be resolved in the same way," Papoulias said, expressing regret at the fact that the whole region had suffered a lot due to conflicts that had not brought anyone any good.
The Greek president welcomed Croatia's European Union membership bid, saying that Greece had been supporting Croatia in this effort from the very start.
"That will be a historic event not just for Croatia, but also for the region in general, because it will form a nucleus of peace in this area," Papoulias said, adding that he had also said this during his recent visits to Romania and Bulgaria.
"Croatia's accession to the European Union will complete the integration of the Western Balkans with the EU as a very important and dynamic part of Europe," he said.
Papoulias said there were great prospects for cooperation between Croatia and Greece in commerce, entrepreneurship and tourism, noting that economic relations between the two countries were currently lagging behind political cooperation.
Asked by a reporter why Croatia was late in joining the EU and NATO, Mesic said that the main reason for the delay was the war that had been imposed on Croatia and its consequences. He added that Europe was heading towards a future where there would be no wars, because the usual motive for war -- territorial expansion -- had been eliminated.
Mesic described European integration as a millennium enterprise based on the interests of both small and big countries, which he said excluded the use of war as a political means.
"Europe is expanding its borders, and that's what we also want to achieve in Southeast Europe. We want to open up our borders and cooperate, and in particular we want to see national minorities as bridges of cooperation, rather than tools for territorial expansion. That's why Croatia advocates speeding up the process of European enlargement," Mesic said.
After the meeting with Mesic, the Greek president held talks with the Speaker of the Croatian Parliament, Vladimir Seks.