The outcome of the referendum opens a new page not only in the relations between Croatia and Slovenia, but it is also "an important message of encouragement to all our neighbours in the southeast of Europe," Kosor told a news conference in Zagreb.
She said that she was now expecting the referendum result to "defuse many tensions and many frustrations".
She recalled that the border arbitration deal separated the process of solving the border issue from Croatia's European Union accession negotiations as "all deadlines from the agreement start running upon the signing of the accession treaty".
Kosor said that she had talked with her Slovenian counterpart Borut Pahor on Sunday and Monday who she said had assured her that there were no more roadblocks in the process of opening the Foreign, Security and Defence Policy chapter within Croatia's EU accession negotiations.
Asked whether she was afraid that the Slovenian parliament might refuse to ratify Croatia's accession treaty, Kosor said that she was now thinking of this moment.
"It is important for us to continue the negotiations and that there were no longer obstacles and blockades," Kosor said adding that in the coming days she would also talk with the head of the Opposition in Slovenia, Janez Jansa.
She recalled that the border arbitration agreement was the result of her agreement with Slovenian PM Pahor.
"The Slovenian PM and I have tried to build bridges and mutual confidence between us and between Croatia and Slovenia in a bid to solve the issue which was on the agenda for 18 years," Kosor said.
The border arbitration deal was signed by Kosor and Pahor in Stockholm last November, and the document has in the meantime been ratified by the two countries' parliaments.
She also welcomed the move by Croatian President Ivo Josipovic who lauded the referendum result as "a victory for Slovenia, Croatia and Europe". While being an MP in the parliament, Josipovic voted against the ratification of the document.
"It is good to see that the President applauded the decision, although he was one of few MPs who voted against that agreement. However, that time is behind us," she said adding that it was important that President Josipovic now backed the decision she and PM Pahor had made.
Kosor went on to say that PM Pahor confirmed his arrival at the Croatia Summit in Dubrovnik in early July which she said would bring together several heads of government.