Mesic said the good relations between the two countries were reflected in frequent meetings on the highest and high levels, "openness in talks" and "concurring views".
He said that neither the world nor Europe were "idyllic and no country entering the European Union is entering a conflict-free environment".
However, "it is crucial that the European Union rules out war as a means of achieving political goals and in the long term ensures development and progress (...) to its members," said Mesic, thanking Hungary for its support to Croatia on its European road.
Gyurcsany said Hungary's most important goal was to help Croatia and other countries in the region become members of the European club.
He said Croatia and Hungary were not linked only by a partly common past but also the present because they shared the most important human, political and social ideas and goals. Hungary sees Croatia as an ally, as a friend, and Hungarians see Croats as brothers, he added.
Democracy will contribute to peace, respect for human and political rights and freedoms as well as cooperation in the region, Gyurcsany said, underlining that everything would be done to achieve that goal.
Also present at the meeting were representatives of the Hungarian minority in Croatia.