Mr Akufo-Addo lost the 2008 presidential poll by one percentage point, but accepted the result.
Earlier, the NPP said it had "enough concrete evidence" to prove that Mr Akufo-Addo had won the election.
And an injury-time chance fell to substitute Eric Addo in the six-yard area, who just could not convert it.
Preliminary results reported by Ghanaian news outlets indicated Mahama was narrowly leading Akufo-Addo, the son of a former president.
Nana Akufo-Addo, the candidate for the New Patriotic Party (NPP), garnered 47.7% of the vote, according to the commission.
But Nana Akuffo-Addo, the losing candidate and now a contender, graciously conceded defeat.
Mr Akufo Addo was a founding member of the NPP and served as foreign minister in 2002-7 under President John Kufuor.
Very tame groups can be observed along the Woodlands-Harpoor Loop in Addo Elephant National Park, but also at many other locales.
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Mr Akufo-Addo, 68, narrowly lost the 2008 election to John Atta Mills in the second round, after leading in the first round.
Born to a prominent family in eastern Ghana - his father, Edward Akufo-Addo, was a chief justice and later president of Ghana.
It mirrors the election four years ago in which Akufo-Addo lost to John Atta Mills with a razor-thin margin after a runoff.
Both Mr Mahama and Mr Akufo-Addo have promised to accept the result, but 5, 000 soldiers have been put on standby just in case.
Striker Nafiu Iddrisu of Ivorian side Asec Mimosas as well home-based players Daniel Addo, Addoquaye Addo and Kwadwo Asamoah were named in the squad.
"Some, such as culling and contraception I would have personally preferred not to consider, " he said at Addo elephant park in Eastern Cape province.
That contradicted what NPP General Secretary Kwadwo Owusu Afriyie had said Saturday night, when he claimed Akufo-Addo had won the presidency with 51% of the vote.
Known as a champion of free-market economics and liberal democracy, Mr Akufo-Addo promises to kick-start an "industrial revolution", extend coverage by Ghana's National Health Insurance Scheme and fight corruption.
Mr Mahama is expected to do well in his home area in the north, while Mr Akufo-Addo draws much of his support from urban areas and the eastern Ashanti region.
Fenaba Addo, a fellow at the University of Wisconsin, recently took a look at the mating habits of college graduates to determine if their tuition bill financing methods impacted their future romantic lives.
"We are ready to concede that in an election that involves more than 11 million voters there might be mistakes, " said Mr Akufo-Addo after the petition was filed at Supreme Court in Accra.
Our correspondent in Accra, Kwaku Sakyi Addo, says that while Ghanaians were ready for a change, the election was also seen as a referendum on Mr Rawlings and the ruling National Democratic Congress (NDC).
The BBC's Sammy Darko in the capital, Accra, says the party has calculated that there were 1.34 million extra votes cast, which if withdrawn from the final tally would make Mr Akufo-Addo the winner.
The candidates who participated in this High Level event include current President and flag-bearer of the ruling National Democratic Congress (NDC), John Dramani Mahama, and his main challenger and leader of the opposition New Patriotic Party (NPP), Nana Dankwa Akufo-Addo.
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