
Enlargement Commissioner Olli Rehn said he hoped such mediation would result in Croatia concluding technical negotiations for membership by the end of this year.
Slovenia has embraced the EU offer, while its bigger neighbour Croatia has said it will decide by March 9 on whether to accept it.
"All previous attempts have failed over the past 18 years and I can't see any other viable way forward, therefore I expect from both countries a positive response," Rehn told a news conference during a visit to Slovenia.
"I can't frankly see why one or another country would want a priori to reject this kind of European facilitation which aims simply at solving the border issue and unblocking the process of the accession negotiation," Rehn said.
He also said no country should set "impossible conditions" for accepting mediation, referring to rumours that Croatia might accept the mediation only if it led to settling the dispute at the International Court of Justice (ICJ) in The Hague.
In December, Slovenia has vetoed 12 chapters, or one-third, of Croatia's accession negotiations. It said the documents Zagreb submitted were prejudicial to the dispute, which dates back to the 1991 break-up of Yugoslavia and hinges on small parts of the two countries' land and sea border.
The European Commission in January asked Nobel Peace Prize winner Martti Ahtisaari, former Finnish president, to help mediate if both parties agreed to it.
Croatia, which hopes to join the EU in 2010, said it would prefer the dispute to be handled by the ICJ but Slovenia rejected that option.
Slovenia, squeezed between Italy and Croatia, wants direct access to international waters in the northern Adriatic. This would force Croatia to cede part of the sea it considers its own.
Last week Slovenia's Prime Minister Borut Pahor met his Croatian counterpart Ivo Sanader for the first time since Pahor took office in November, but they failed to agree on a way forward.
The row has also complicated Croatia's NATO membership bid, although Slovenia ratified Croatian accession in February.
A Slovenian non-parliamentary nationalist party demands a referendum on the issue, saying Croatia should not be allowed to join the alliance because of the border dispute. The demand could delay Croatia's NATO entry, which is planned for April.
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