The South West Africa People's Organisation was concerned on Saturday that many voters were not able to cast their vote due to technical glitches.
"The Swapo Party has become aware of many voters who were turned away from polling stations across the country while expecting to cast their votes," Swapo information secretary Helmut Angula said in a statement.
"This is a worrying and disturbing situation. This could also affect the credibility of the elections.
"Swapo therefore demands that the electoral commission explain this situation and also assure the nation that this will not have a negative impact on the entire elections."
Results were trickling in at a snail's pace at the election centre in the capital Windhoek.
Problems with the functioning of hand held scanners verifying voter cards and fingerprints of voters caused huge delays with long queues at polls seen deep into the night on Friday.
"Voting at three polling stations ended on Saturday morning, including at the voting in the central prison of Windhoek," said chief election officer Paul Isaak.
Votes from only eleven of 121 constituencies had been verified and released.
Provisional results from some fifty polling stations indicated that Swapo received slightly fewer votes than in 2009.
A neck-on-neck race unfolded between the current official opposition party Rally for Democracy and Progress (RDP) and the DTA (Democratic Turnhalle Alliance) for second and third place.
A similar picture unfolded for the presidential race with incumbent Prime Minister Hage Geingob and Swapo candidate leading the vote.
The DTA president McHenry Venaani, 37, and Hidipo Hamutenya, 75, of RDP were competing for second and third positions respectively.