"We should sit at the negotiating table and reach an agreement, and if that is not possible, we should seek arbitration," Mesic said during a visit to a construction site near Zagreb.
Any imposition of a solution by force, particularly if it involves politicians, cannot bring about a positive result," the president added.
Asked how the incident would affect cooperation between Croatia and Slovenia, Mesic said that the cooperation was good at the moment and that it would stay that way in the future. "This is an open issue which can be resolved through negotiation," he said.
Mesic recalled that the Badinter Commission had decided that the land borders of the former Yugoslav republics should be treated as the borders of the newly independent states.
"The border between Croatia and Slovenia was thereby defined. Not every metre of it is marked and the land border is yet to be demarcated. We must agree on the sea border, and if we cannot, the matter goes to arbitration," Mesic said, adding that he was confident the European Union would say the same.
Asked if he thought that the Slovene politicians involved in the incident went beyond good taste, the president agreed that they had overstepped the mark.
The incident happened on Wednesday afternoon when a group of 12 Slovene nationals illegally crossed the border near the Plovanija border crossing in the Croatian part of Istria to visit Josko Joras, an ethnic Slovene who claims that his house is located on Slovene territory.
On their way back, the Slovenes again bypassed the official border crossing point, but were stopped by the Croatian police and taken to the police station in Buje for questioning. After that they were escorted back to the Slovene border. Among the Slovenes were members of the People's Party and its leader Janez Podobnik. Joras is also a member of this party.