The two presidents spoke to the press on Thursday in a break of an informal meeting at Rasica, 30 km south of Ljubljana.
"We took note of the fact that there is no progress in the last two outstanding issues... They are complex issues, but it is worrisome that the governments are not even trying to close them," said Drnovsek, adding that his meeting with Mesic was an incentive to the two governments to sit at the negotiating table again.
Drnovsek recalled that 15 years ago Slovenia and Croatia enjoyed excellent cooperation on their roads to independence and that now it was "high time" to reach solutions which should be constructive and which did not create the feeling that there was a winner and a loser.
President Mesic underlined that the two governments had the task to close outstanding issues.
The press asked if his opinion on the possibility of a border deal differed from the position of the Croatian government, which suggested that this issue be closed via an international judicial institution, and whether this issue could be closed bilaterally after 15 years of failures.
Mesic said he felt there was still room for negotiations and a possibility to avoid arbitration.
"We call on the governments to sit down and try to settle this," he said.
Asked about the White Book on the border, which the Slovene Foreign Ministry issued last week, Mesic said it was arguments that were important in politics.
Both presidents criticised some Slovene political parties and groups advocating that Slovenia should make its support for Croatia's accession to the European Union conditional on the border issue.
"Those are two separate things which have no relation to one another," said Drnovsek, adding that such setting of conditions or blackmailing would obstruct constructive and good relations.
Mesic said he and Drnovsek cooperated from the time when both were members of the presidency of the former Socialist Yugoslavia. Both said the Croatian and Slovene peoples and states were close and that good neighbourliness was their destiny. They
also advocated intensifying political and economic cooperation.
Slovenia has achieved its strategic goals by joining the EU and NATO, said Mesic, adding that Croatia too wished to join the two institutions, and that drawing closer to the Union would strengthen stability and cooperation in the entire region.