Supporters of the leading candidates are confident of victory
The Electoral Commission of Ghana is due to announce the results of Sunday's presidential and parliamentary polls.
The presidential race is tight with results so far giving governing New Patriotic Party (NPP) candidate Nana Akufo-Addo a slender lead on 49.3%.
But opposition National Democratic Congress (NDC) contender John Atta Mills is just behind on 47.8% of the vote, with almost all the results in.
If neither candidate passes the 50% threshold a second round must be held.
Partial official results from 211 of the 230 electoral constituencies put Mr Akufo-Addo in the lead with 3,902,037 votes against 3,777,812 for Mr Atta-Mills, according to the Electoral Commission of Ghana website.
Results must be announced by 1700 GMT on Wednesday, at the expiry of a 72-hour deadline since polls closed.
The BBC's Will Ross in the capital, Accra, says the election campaigns were expensive but if there is to be another poll later this month, the two main parties would have to find more money to woo voters.
He adds that although largely peaceful and widely praised by observers, the elections have raised tension in Ghana and the stakes are high - the nation has just discovered oil.
There is also a tight race in the parliamentary election.
In recent years the NPP, the governing party, had a clear majority but the opposition NDC has closed the gap and could gain control of the parliament.
Some results have been disputed, raising the risk of a peaceful poll turning acrimonious, and there have been isolated reports of violence.
On Tuesday, the NDC accused the governing party of plotting to rig the poll - a charge the NPP branded false.
There were eight candidates to succeed President John Kufuor - who steps down in January having served the maximum two terms - but the election has been a two-horse race, says our correspondent.
There was a poor showing for third-place candidate Papa Kwesi Nduom, of the Convention People's Party, who had been seen as a possible kingmaker or spoiler.
Turnout was high for Ghana's fifth set of elections since embracing multi-party democracy in 1992.
The former British colony was the first African state to gain its independence in 1957.
A nation of 22 million people, it is the world's second biggest cocoa grower and Africa's number two gold miner.