The electoral commission has yet to announce the results of parliamentary elections also held on Sunday.
Representatives of both the NDC and the NPP said on Wednesday that their counts from the voting indicated that the NDC had won at least 115 seats in the 230-seat national assembly.
A victory for the opposition in parliament combined with a presidential win for the NPP would lead to a divided government in Ghana.
Sebastian Spio-Garbrah, an analyst with the Eurasia Group, said such an outcome would "create regular tensions around yearly budgets, ministerial appointments and privatisations".
The NDC earlier in the week accused the ruling NPP of trying to rig the election with the help of the country's security forces, an accusation both the NPP and the military have denied.
International election observers called the vote "open, credible and peaceful" and said Ghana offered the hope the African continent needs in the aftermath of troubled elections in Kenya and Zimbabwe.
"Ghana is becoming a model of democracy in the region and abroad," Ketumile Masire, the former president of Botswana, said in a statement from the Carter Center observer mission.
John Kufuor, the current president of Ghana, steps down in January after the maximum two terms.
His successor takes over as Ghana looks to an era of greater prosperity with offshore oil set to become a significant factor in the economy late in 2010.
Reporting from Accra, Al Jazeera's Ama Boateng said: "The discovery of oil off the coast of Ghana has the potential to really transform the country's economy.
"The country is growing and people want to see this improvement in their daily life … it's not just about economic prosperity but also about economic distribution."