President Cyril Ramaphosa said that members of the Umkhonto we Sizwe (MK) party, backed by his predecessor Jacob Zuma, who are threatening to riot if they are not allowed to contest the elections in late May, will be arrested.
He added that the government hears threats to destabilize the country, but law enforcement agencies are taking action against the "enemies of the democracy" who make threats.
"I just want to make it clear to anyone who is threatening any form of unrest, there will be follow up and they will be arrested," Ramaphosa said. "Those are people who belong in jail, they are the people who are the enemies of our democracy."
The president added that the people of South Africa value their hard-won democracy, do not want instability, and have always followed the rule of law.
On Wednesday, MK official Visvin Reddy warned that failure to allow the party's candidates to contest the election would end in "civil war."
"Hear me very carefully, this country will be turned into civil war the day the MK party is not allowed to campaign and to be on the ballot paper. No one will vote we will make sure that no one will vote," he said. "We are sending a loud and clear message that if these courts stop MK, there will be anarchy in this country, there will be riots like you've never seen in this country."
In response, the director general of the South African Electoral Commission, Sy Mamabolo, said that if the party does not comply with the electoral code of conduct, its leaders would be punished or imprisoned.
Later, in an interview with a local publication, Reddy said that his words had been taken out of context and that the video of his remarks had been edited.
Last December, Former South African President Jacob Zuma said he will support the Umkhonto we Sizwe, named after the former paramilitary wing of the African National Congress (ANC) during the apartheid struggle.
Umkhonto we Sizwe was the paramilitary wing of the ANC, founded by Nelson Mandela in 1961 to fight against the apartheid regime in South Africa. It was labeled a terrorist organization by the white minority government and banned until 1990. The MK was disbanded in 1993 after the end of apartheid. Jacob Zuma was a member of the MK and served as its intelligence chief.
South Africa's general elections are to be held on May 29, when citizens will vote for a new National Assembly and provincial legislatures.