The Tain vote is crucial to the outcome of the presidential race
Provisional results from the last constituency to vote in Ghana's presidential run-off election point to a victory for the opposition.
Electoral officials in Tain said the opposition's John Atta Mills won 19,566 votes, with 2,035 votes cast for governing party rival, Nana Akufo-Addo.
In the election overall, Mr Mills has a narrow lead over Mr Akufo-Addo.
The final results from the national election are expected to be declared later on Saturday.
The BBC's Will Ross in the Ghanaian capital says allegations of rigging had been made by both sides and the electoral commission said it would examine any evidence before giving the final result.
Mr Akufo-Addo's lawyers have been trying to stop a final result being announced.
His New Patriotic Party (NPP) had also sought an injunction to prevent Friday's ballot in Tain, claiming conditions in the remote rural constituency in north-west Ghana were not conducive to a free and fair election.
Earlier, the outgoing President, John Kufuor, urged both candidates to respect the final result.
He appealed for calm and said any complaints of vote-rigging should be dealt with by the courts after the new president is sworn in on Wednesday.
There is growing pressure on the governing party to accept the outcome of the election and to avoid stalling the process, our correspondent says.
RIVALS AT A GLANCE
JOHN ATTA MILLS (left)
Party: National Democratic Congress
Executive posts: Vice-president 1997-2000
Profession: University professor
Hobbies: Hockey, swimming
Family: Married with one child
NANA AKUFO-ADDO (right)
Party: New Patriotic Party
Executive posts: Attorney general 2001-03; foreign affairs minister 2003-07
Family: Married with five children
Mr Kufuor spoke out amid heightened fears of poll-related violence, urging both candidates to avert a constitutional crisis.
He is stepping down after serving the maximum two terms in office and his successor is due to take office on 7 January.
Soldiers and police were deployed across Tain, where a problem with distributing ballots prevented voters from taking part in last Sunday's run-off.
Ghanaian state radio reported that NPP agents with loudhailers had toured towns and villages in the district on the eve of voting urging supporters to boycott the poll.
The party's attempts to block the ballot were criticised by civil groups.
Mr Atta Mills of the National Democratic Congress (NDC) won the area in the first round of voting on 7 December and the NDC is confident of victory.
He has 50.13% of the approximately 9m votes cast on Sunday, compared with 49.87% for Mr Akufo-Addo - a gap of just over 23,000 votes.
Mr Akufo-Addo won the first round in the national result but not by enough to avoid the run-off.
The NPP has complained of alleged intimidation during voting in the Volta region, while the NDC claimed there had been vote-rigging in the Ashanti area.