Georgian President Mikhail Saakashvili, elected this year after a bloodless revolution, has pledged to return the mountainous sliver of land bordering Russia to central rule.
But candidates and voters were united in proclaiming their unrecognised Black Sea state independent.
"Abkhazians are voting for their future of their country so the country can be independent and the people can be free," said Sergei Bagapsh, main rival to Russian-backed candidate Raul Khadzhimba, after slotting his voting slip into a transparent ballot box in the capital Sukhumi, where turnout seemed high.
The poll was certain to increase a tangle of tensions in the Caucasus region, which Russian President Vladimir Putin considers strategically crucial.
West-leaning Georgia accuses Moscow of double standards in supporting Abkhazian separatists while cracking down on its own rebels in Chechnya, a region Russia says is on the frontline of the so-called war against terrorism.
Tbilisi points to Chechnya and says
Moscow is hypocritical
Russia has given three-quarters of Abkhazians passports and pays local pensions. A meeting between Khadzhimba and Putin, widely displayed on the Abkhazian candidate's campaign posters, rankles with the Georgians.
But Tbilisi pledged not to disrupt the poll: "We do not intend to raise obstacles [to this election]. The main thing is that these elections are not legitimate," Georgian State Minister Goga Khaindrava told Ekho Moskvy radio on Sunday.
Abkhazia has enjoyed de facto independence since local forces, aided by Russian volunteers and weapons from the ex-Soviet military, defeated the Georgian army 11 years ago.
Local media reported a mortar attack in an ethnic Georgian village on Sunday but Russian and UN peacekeepers say that, despite Saakashvili's fiery rhetoric, the ceasefire line has quietened down since he came to power and clashes are rare.
The legacy of fighting in the eerily deserted region, abandoned by most of the ethnic Georgian half of the population after the war, is everywhere.
Saakashvili wants to return the
region to Tbilisi's rule
Scars from bullets and heavy weapons disfigure houses in Sukhumi. Once grand buildings in what was a Soviet resort stand open to the sky, their ground floors rank with weeds.
Outside the capital, roads are largely empty. Cows laze on tarmac still pitted from the treads of tanks, blinking at the occasional passing car.
The region has suffered economic collapse and gets by on an annual budget of a mere $15 million, but officials press on with their dream of independence.
"Other countries have split apart - the Czech republic and Slovakia divorced peacefully - why can't Abkhazia be a normal free country?," said Khadzhimba after voting in the first multi-candidate elections the region has seen.
Ethnic Georgian voters seemed to largely support such calls, saying they were fed up with struggling to survive in depressed rural areas where ruined houses stand in uncultivated fields.
"I voted for peace, freedom. We do not want another war. We just want a good president who looks after us," said Dmitry Gogiya, 27, after voting in the ethnic Georgian town of Gali, where many women have worn the black of mourning since the war.
But Saakashvili has kept tension cranked up, threatening this summer to fire on Russian holidaymakers sailing to Abkhazian resorts.
He says the region has been "ethnically cleansed" and that most of the 250,000 Georgian refugees are still not allowed home.
But Abkhazia thinks it is too strategically important for Moscow to ignore while Washington supports Georgia with aid and military training.
"The deeper America goes into Georgia, the deeper Russia will go into Abkhazia," said Maxim Grinjia, a deputy to Abkhazia's top foreign affairs official.