The Umkhonto weSizwe party says it is unhappy with the way the election results were conducted and has raised several concerns with the Independent Electoral Commission (IEC).
The party has said it will approach the electoral tribunal over the matter.
MK is calling for the votes to be counted manually immediately.
The company said it rejects the results currently displayed on the IEC results board.
Party spokesman Nhlamhlo Ndlela said the decision had been communicated to party leader Jacob Zuma.
Ndlela said the election results do not reflect the party's actual electoral performance.
Early on Friday morning, both the IEC result board and website were down for over an hour.
The cause of the crash is still unknown, but the IEC said it is investigating the cause of the crash.
Zuma's MK party has established itself as one of the ANC's biggest challengers in this election.
The party made significant gains, beating both the ANC and the IFP in KwaZulu-Natal.
Meanwhile, the IEC said on Friday that the election results would not be announced on Saturday due to objections and appeals.
IEC deputy CEO Mawethu Mossery said the commission had received more than 100 challenges.
Below is the full media briefing: