People in Georgia's breakaway province of Abkhazia have cast their ballots in a re-run of October's disputed presidential election.
Mr Bagapsh said some voters had been turned away
The two main rivals from that round, Sergei Bagapsh and Raul Khadzhimba, are running on a joint ticket in a Moscow-sponsored compromise.
Early reports say they won the support of about 60% of voters.
Georgia does not recognise the vote in a territory which has had de facto independence for more than a decade.
Polls closed at 2000 local time (1600 GMT) on Wednesday.
Preliminary reports suggested the turnout was over 50%, indicating that the vote was valid.
Mr Bagapsh, who claimed victory in the first vote, is leading the joint ticket against Yakub Lakoba, who came last in October.
Mr Bagapsh said some voters with absentee ballots had been turned away at polling stations, which could affect turnout. The issue would be raised with the Abkhaz election commission, he told French news agency AFP.
Security is reported to have been tightened in border areas.
The BBC's Natalia Antelava says the outcome is fairly predictable, as the man who opposes Mr Bagapsh and Mr Khadzhimba received only 500 votes in the October election.
Mr Bagapsh has promised to fight corruption, establish law and order and improve the economy of the impoverished Black Sea province.
He also says that his former rival, pro-Moscow Raul Khadzhimba, will become the vice-president.
Our correspondent says this is the Kremlin's solution to the political stand-off, and a way of ensuring that under Mr Bagapsh, Abkhazia does not move away from Moscow's control.
For years, Russia has been the only lifeline and a major influence on life and politics in the isolated and unrecognised Abkhazia.
When official results in October showed that the Abkhaz people had voted overwhelmingly against Mr Khadzhimba, Russia imposed economic sanctions and insisted on a re-run.
Tbilisi has condemned Moscow for sending observers to Abkhazia, and called on the Kremlin to stop what politicians there say is meddling in Georgia's affairs.