The race is tight with President John Mahama and his rival Nana Akufo Addo running neck and neck in opinion polls.
Ghana’s electoral commission said the agency would start releasing results on Thursday from a presidential and parliamentary vote held the day before as the main opposition party claimed an unassailable lead and called on President John Mahama to concede defeat.
The majority of polling stations closed at 5pm local time (17:00 GMT) on Wednesday, officials said, and counting was under way on Thursday.
Al Jazeera’s Nicolas Haque, reporting from the capital, Accra, said the delay in announcing the results was due to “over-voting”, according to the election commission.
“The opposition is putting pressure on the election commission to announce numbers but nothing has been made public yet,” he said.
“The election commission has come out saying there has been over-voting and they have to put a process in place to look into that. This is what is causing the delay.”
The contest between incumbent John Mahama and his rival Nana Akufo-Addo is said to be very close, with both sides reportedly having won 48 percent of the votes so far.
According to the opposition, the delay “gives suspicion that the commission is trying to overturn the clearly expressed will of the people”, spokesman Sammy Awuku told a news conference broadcast live on radio stations.
“We call on the youth of our country to remain calm. We also say the electoral commission has a responsibility to … restore sanity to the process.”
The elections come at a time of severe economic decline in the West African country, and amid a volley of accusations of financial mismanagement on the part of the ruling party.
For years, Ghana was one of Africa’s most dynamic economies. But it slumped in 2014 as commodity prices fell, and a fiscal crisis widened the budget deficit and elevated inflation.
Akufo-Addo’s New Patriotic Party says the government has mismanaged national finances, including revenue from oil from an offshore field operated by British company Tullow that became operational in 2010.
The government has denied the accusations and urged voters for vote for it, arguing that growth would return to at least 8 percent in 2017.
At least 15 million people were registered to vote in the election.
Initial reports showed few voting problems, according to the Coalition of Domestic Election Observers. But voting was re-scheduled for Thursday in Jaman North constituency in Brong Ahafo region because of security concerns and logistical problems.
There are seven presidential contenders, including five minor candidates. In a parallel parliamentary vote, 275 seats are being contested.
Elections in Ghana are famously close races. Mahama narrowly won in 2012 with 50.7 percent.