Ghanaian President John Kufuor has urged both candidates in the election to choose his successor to respect the result, as the last constituency voted.
Mr Kufuor 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.
The opposition leader, John Atta Mills, has a narrow lead over the governing party candidate, Nana Akufo-Addo.
Mr Akufo-Addo's lawyers are 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 were not conducive to a free and fair election.
'Constitutional crisis'
But the BBC's Will Ross in Ghana's capital, Accra, says there is growing pressure on the governing party to accept the outcome of the election and to avoid stalling the process.
President John Kufour 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.
Polls closed at 1700 GMT in Tain, which could not vote in last Sunday's run-off because of a problem distributing ballots.
Soldiers and police were deployed across the district - the last of Ghana's 230 constituencies to vote.
The electoral commission is not expected to announce the outcome from the constituency, along with the presidential result, until Saturday at the earliest.
'Loudhailers'
Ghanaian state radio reported that NPP agents with loudhailers had toured towns and villages in the district on Thursday night urging supporters to boycott the vote. The party's attempts to block the ballot were criticised by civil groups.
Our correspondent says Mr Akufo-Addo cannot realistically win enough support among Tain's 53,000 eligible voters to overturn the lead held by Mr Atta Mills of the National Democratic Congress (NDC).
Mr Atta Mills won the area in the first round of voting on 7 December and the NDC is confident of victory.
RIVALS AT A GLANCE
He has 50.13% of the approximately 9m votes already cast, compared with 49.87% for Mr Akufo-Addo.
Just over 23,000 votes separate the two candidates.
Mr Akufo-Addo won the first round in the national result but not by enough to avoid the run-off.
Officials from the NPP have been meeting and election observers suggest the party is now split on whether Mr Akufo-Addo should accept defeat, says our correspondent.
The head of West African body Ecowas has said that in the interests of the country the candidate with the least votes should concede by the end of Friday.
Mohammed Ibn Chambas told the BBC: "I believe that there comes the moment when each politician and each political party should place the supreme interest in the country to keep the stability of the country over and above their own interests.''
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.
The electoral commission had said it would investigate those claims if provided with evidence.
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