The European Commission on Monday urged Zagreb to respect a recent arbitration ruling that gave Slovenia key access to international waters off Croatia's coast and drew a maritime border between the two EU member states.
Croatia has repeatedly said it will not implement the June ruling by an EU-backed special tribunal in The Hague.
"It's very important for two member states, for the EU and for the region as such that the ruling of the arbitration is respected and implemented fully," the European Union's foreign policy chief Federica Mogherini said on the sidelines of a western Balkans conference in the Slovenian lake resort of Bled.
"It's important... to show to the rest of the region that rules are to be respected," she added.
The area under dispute is a tranquil bay on the northern Adriatic Sea, where the medieval buildings of the southwestern Slovenian town of Piran tumble down to a sleepy port.
But the bay is also shared by Croatia, and the dispute over where the sea borders should be drawn has poisoned relations between the neighbours since they both declared independence from Yugoslavia in 1991.
In 2009, the two countries signed an EU-supported deal to allow the arbitration court in The Hague to solve the row over the 13 square kilometres (five square miles) of largely uninhabited land and Piran Bay.
Zagreb had only agreed to join the proceedings after Ljubljana lifted its veto in 2009 to Croatia's accession to the European Union. But it pulled out again in 2014 following a phone tapping scandal.
Zagreb insists it does not recognise the June ruling, which awarded Slovenia uninterrupted access to international waters as well as a larger stake of the Piran bay, currently divided in half by the warring neighbours.
European Commission vice-president Frans Timmermans warned Monday that Brussels "will insist with both parties that the implementation... is the best possible outcome of this process".
"Let me remind you that when we discussed enlargement of the EU with Croatia, arbitration was one of the conditions set upon enlargement," Timmermans said in Bled.