The claims, made by the New Patriotic Party, come as preliminary results indicate a tight race between their candidate, Nana Akufo-Addo, and incumbent President, John Dramani Mahama.
Local news outlet Joy News used counts from polling stations to predict a slight victory for Mahama.
The opposition on Sunday called for an audit of the results before they are officially released.
International observers have said the vote appeared to be transparent and peaceful even though voting continued into a second day on Saturday because of logistical and technical problems.
This is the first election where Ghana has used a new biometric registration system which scans fingerprints to identify registered voters.
In addition to the presidential race, voters were choosing 275 members of parliament, where President Mahama’s National Democratic Congress has held a majority of seats.
Challenger Akufo-Addo leads the New Patriotic Party, which narrowly lost to the late President John Atta Mills in 2008. He has campaigned on a promise to provide free senior high school education for all.
Ghana‘s law stipulates that results must be announced within a 72-hour period after polling ends.
If no presidential candidate wins a clear majority, a runoff is planned for December 28.
The west African country has earned a reputation for stability recently in an often turbulent region because of its recent record of peaceful, democratic transfers of power.
Ghana is also one of Africa’s fastest growing economies and is beginning to benefit from commercial oil production that began in 2010.
But many residents, complaining of high living costs and low wages, say they now want more immediate benefits from the country’s oil wealth, which is expected to grow rapidly in the coming years.