By visiting Montenegro, Josipovic began a Balkan tour which will also include visits to Macedonia and Kosovo.
The issue of the Croatian-Montenegrin border on the Prevlaka peninsula is one of the outstanding issues, but the two presidents said it was not a "burning political issue" which would undermine the two countries' relations and that it was being dealt with by intergovernmental commissions.
"We didn't talk about Prevlaka but the border, and the border issue is more than just Prevlaka," Josipovic told a joint news conference.
"We know that the intergovernmental commissions are working intensively. There are different opinions as to where the border should be. The agreement is absolutely clear, if the commissions find no common ground in the expectations on both sides, (we go) before the international court in The Hague. That's where states solve their outstanding issues and disputes when they can't agree," Josipovic said.
He said there was a difference of opinion and that Croatia had similar differences with Bosnia, Serbia and Slovenia. "It's not a burning issue. We don't have bad or deteriorating relations because of it. We know it's a problem that needs solving and we will solve it."
"This issue doesn't burden our relations," said Vujanovic. "We solved it with the 2002 interim regime which is working without state treaties."
He thanked Croatia for supporting Montenegro's Euro-Atlantic integration aspirations. "This support has been important and we highly appreciate Croatia's willingness to continue to promote our integration interests, now in a new position, as a European Union member, and before as a NATO member."
Josipovic also met with Montenegrin Prime Minister Milo Djukanovic and Parliament Speaker Ranko Krivokapic.