Addressing Slovene ambassadors at regular annual consultations in Brdo Pri Kranju on Thursday, Drnovsek said the border issue with Croatia had turned into a chronic problem which would have to be dealt with this year again.
"It's time this issue was taken off the agenda and it wouldn't be good to have it burdening us when we will be chairing the Union."
Drnovsek said Slovene diplomats should reach an "honest agreement" with Croatia to attempt once again this year to settle the border dispute with a bilateral agreement and if that was not possible, go to international arbitration.
He also said Slovenia's presidency of the Organisation for Security and Cooperation in Europe last year had been successful.