The European Union does not recognize the constitutional and legal framework within which the presidential elections in the breakaway Georgian region of Abkhazia have taken place, EU High Representative Catherine Ashton said on Saturday.
"The European Union reiterates its support to the territorial integrity and sovereignty of Georgia, as recognized by international law," she said.
"The European Union would in this context like to emphasize the importance of the Geneva International Discussions in ensuring the security and stability in the region."
Alexander Ankvab has won the presidential election with 54.9% of the vote, Central Electoral Commission chief Batal Tabagua said, announcing the final tally earlier in the day.
The turnout was 72%.
The runners-up were Prime Minister Sergei Shamba and purported opposition leader Raul Khadzhimba.
All the three are against any reunification with Georgia.
Abkhazia went to the polls on Friday following the death of President Sergei Bagapsh in May.
Russian President Dmitry Medvedev congratulated Ankvab on his victory but Tbilisi called the polls illegitimate and NATO said it would not recognize them.
"The alliance reiterates its full support for the sovereignty and territorial integrity of Georgia within its internationally recognized borders," NATO Secretary-General Anders Fogh Rasmussen said.
Russia has thousands of troops in Abkhazia and issues Russian passports to its residents.