As of 8 p.m. Tuesday, President Akufo-Addo maintained his slim lead over Mr Mahama.
Ghana's ruling party, the New Patriotic Party, and the opposition National Democratic Congress have claimed victory in Monday's general election.
Ghanaians went to the polls on December 7 to elect a president and parliamentarians.
President Nana Akufo-Addo of the New Patriotic Party is contesting against former president John Mahama of the National Democratic Congress and 10 other aspirants.
As of 8 p.m. Tuesday, President Akufo-Addo maintained his slim lead over Mr Mahama, polling 4,113,529 votes (49.61 per cent) against Mr Mahama's 4,066,272 votes (49.04%), according to results announced at the constituencies. At the end of collation, the candidate who secures 50% plus one vote will be declared the winner.
At the parliamentary election, however, the NDC is edging the NPP narrowly, with 87 seats to the ruling party's 84. The results of 173 constituencies have so far been collated. After the collation at the 275 constituencies, the results will be taken to the 16 regions, before the final collation at the national level by the electoral commission.
Ahead of the election, Jean Mensa, the chairperson of Ghana's Electoral Commission, assured that the final result, if everything goes well, would be declared 24 hours after the close of voting on Monday. But on Tuesday evening, the commission backtracked, saying it would be extending the intended timeline for the declaration of the results.
"The new timeline will be communicated shortly," the commission said in a statement.
Victory 'on both sides'
On Tuesday morning, while official results showed Mr Akufo-Addo in a narrow, early lead, the opposition held a press conference to announce they had won majority seats - 141 out of the total 275 - in the parliament.
Asiedu Nketia, the NDC general secretary, told journalists that the win gives the party "absolute control of the House."
At the NDC headquarters in Accra, supporters were already in a celebratory mood as they awaited the final announcement by the electoral commission.
Kakra Essamuah, the party's director of communications and administration, said they are getting "credible and reliable" results from their agents across the country.
"We are in a firm position to be able to make certain tentative conclusions and that is that we think we won this election," Mr Essamuah told PREMIUM TIMES on Tuesday afternoon.
"So far we have done a few calculations and we think we are having majority of seats in parliament. In this country, it's not possible to have majority of seats in parliaments and now win the presidency."
A few kilometres away, at the secretariat of the ruling NPP, a large crowd of supporters watch a live transmission of the election on a large screen. Inside one of the offices, some party executives celebrate with glasses of wine.
Collins Nuamah, a senior NPP official, told PREMIUM TIMES that the NDC claim of winning parliamentary majority is a figment of the opposition's imagination.
"The NDC doesn't have a system," said Mr Nuamah, director of finance and administration at NPP.
"We have proven over time that we have a system that will take account, tracking results from the polling stations to electoral areas to the constituencies to the regions and to the national.
"They are just throwing dust in the eyes of the Ghanaian people and the international world. we have a system, I can tell you authoritatively that as of this hour we have collected and collated about 98 per cent of the results nationwide."
Mr Nuamah said the NPP is a law-abiding political party and, as a result, would not preempt the electoral commision by announcing the results.
"But we know that President Nana Akufo-Addo per what we have collated we know that the NDC can never beat or undo what has been established by the Ghanaian people.
"I am telling you authoritatively that per our system and structure, and this has been proven over time, that Nana Akufo-Addo at 5 p.m. will be declared president-elect for the 2020 election. We are certain."