The two presidents held a news conference after their second informal meeting this year, held in Miljana, in Zagorska Sela municipality, on the Croatian side of the border.
President Mesic said that the meeting focused on a number of issues, including the situation in the region, the 30th anniversary of the Osimo Accords, and outstanding issues.
"I intentionally did not use the word 'problems' but 'outstanding issues', because those issues can be solved," Mesic said.
The Croatian-Slovene border dispute can be solved by freezing the current situation, finding a transitional solution, or having it settled before the International Court of Justice in The Hague, Mesic said.
"I believe a solution could be found if experts from both countries sat down at the negotiating table and, unburdened by politics, determined the land border with the help of existing documents, if our government accepts that way of dealing with this issue," Mesic said.
"Once the land border is identified, the sea border can be identified with mathematical precision by applying international conventions," Mesic said, reiterating that this would be the best solution.
If this approach fails, we should have the matter settled by an international court or through arbitration, Mesic added.
Commenting on the two countries' relations, Mesic said that cooperation between Slovenia and Croatia was good, but that the media were often placing emphasis only on outstanding issues.
Drnovsek concurred, saying that there were numerous examples of cooperation between the two countries.
He reiterated that a bilateral agreement on the border issue would be the best solution, but that the two countries should turn to the International Court of Justice if they proved unable to solve the dispute bilaterally.
"We don't want to be part of the problem, we want to be part of the solution and help the EU solve some other issues in Southeast Europe which are much more complex," Drnovsek said.
Asked whether Slovenia was facing a political crisis due to the fact that his position differed from the position of Prime Minister Janez Jansa and Foreign Minister Dimitrij Rupel, Drnovsek answered in the negative.
"There will be no crisis over that issue. We have an ongoing dialogue with the government regarding those issues and it is normal that our views sometimes differ," Drnovsek said.
The Osimo Accords settled all outstanding issues between Italy and the former Yugoslavia, with Croatia and Slovenia being successor states to the former Yugoslavia, and the Accords are in effect and cannot be changed, Drnovsek said.
Signed 30 years ago today, the Osimo Accords solved all outstanding border issues and questions regarding the property of Italians who left Yugoslavia after World War II.
Apart from its symbolic importance, the anniversary also has practical importance.
"Its practical importance is that those issues cannot and must not be reopened," Drnovsek said commenting on reports that during Croatia's EU accession talks Italy would try to claim back the property of ethnic Italians in kind, instead of in money as agreed under the Osimo Accords.
Drnovsek said that during its EU accession talks Slovenia had resolutely dismissed any such attempts and that Croatia had the right to take the same position.
Under the Osimo Accords, Italy accepted to have Italians who left the former Yugoslavia compensated in money, instead of claiming back their property.
"This was confirmed by the Rome Accords of 1983, which form a firm legal basis that is still in force and that cannot be changed if we respect international law," Drnovsek said.