The Permanent Court of Arbitration in June ruled that most of the Piran Bay area shared between the two neighbours was Slovenia's territorial waters, and that Slovenia should have a sea corridor through Croatian waters to international waters.
The Hague-based court's six-month deadline for the states to implement the ruling expires on Dec. 29. Croatia rejects the ruling, saying it withdrew from the process in 2015 because of Slovenia's violation of the arbitration procedure.
"We intend to implement the ruling and expect Croatia to do the same," Slovenian Prime Minister Miro Cerar said at a news conference following talks in Zagreb on Tuesday with his Croatian counterpart Andrej Plenkovic.
"Slovenia will start the implementation where it can do it alone, and it will seek dialogue and cooperation from Croatia where it cannot act alone."
Plenkovic said the ruling was not obligatory for Croatia, which had withdrawn from the arbitration process after a leaked tape showed that a Slovenian judge on the arbitration panel had improperly exchanged confidential information with the Ljubljana government.
The court acknowledged the arbitration violation but concluded that it was not serious enough to halt the case.
"The issue of borders is an open issue for Croatia," Plenkovic said, adding that Croatia had proposed to Slovenia a legal framework for new talks on the borders. Cerar dismissed the idea, saying the arbitration ruling was final for Slovenia.
Plenkovic warned against "unilateral acts that could cause incidents on the borders".
The two countries have been arguing over their sea and land borders since both declared independence from former Yugoslavia in 1991 as it disintegrated and slid into war.
The dispute held up Croatian accession to the EU for many years. Only after both parties agreed to arbitration was Zagreb granted entry to the bloc in 2013.
The court ruled that Slovenia should have most of the Piran Bay area recognised as its territorial waters.
In addition, the tribunal established a 2.5 nautical mile-wide and some 10 nautical mile-long corridor through Croatian waters to give Slovenia much-coveted direct access to international waters.