Opposition protesters were dispersed from outside the commission's offices in Accra by police firing tear gas.
The NPP said in a statement that the National Democratic Congress had stolen votes across the country.
NDC candidate President John Mahama had a narrow lead over NPP rival Nana Akufo-Addo, according to local media.
Joy FM said based on partial results Mr Mahama looked likely to gain more than 50% of the vote, which would give him overall victory without needing a run-off vote.
Ghana, one of the world's fastest growing economies, is regarded as one of Africa's most stable democracies.
Mr Akufo-Addo lost the 2008 presidential poll by one percentage point, but accepted the result.
However, his party said they had "enough concrete evidence" to prove that he actually won this year's election.
"The ruling NDC conspired with certain EC staff in constituencies across the country to falsify the election results and thereby abuse the mandate of the people of Ghana," the party said.
"It was this planned, systematic stealing of votes at the collation level that was, thankfully, discovered in time."
The party cited discrepancies between initial tally sheets and the results reported in the media.
It said thousands of votes had been stolen from Mr Akufo-Addo and added to Mr Mahama's tally.
The opposition demanded an inquiry before official results are released.
Election commissioner Kwadwo Afari-Gyan told Reuters news agency he was not yet aware of the NPP complaint.
The NDC has not yet responded to the allegations.
Observers said Friday's vote, for a new president and parliament, passed off  in a largely peaceful manner.
Some glitches with a new finger-printing system meant that voting continued into Saturday in some parts of the country.
The turnout was reported to be high, at roughly 80%.
As a top exporter of cocoa and gold, Ghana is one of the world's fastest-growing economies.
In 2011 it saw economic growth of 14% and experts predict growth of 8% for 2012 and in 2013.
Ghana's opposition New Patriotic Party has accused the governing party of conspiring with Electoral Commission staff to fix Friday's election.