Several government buildings and hospitals in the KwaZulu-Natal province are being picketed by public servants as part of a nationwide strike over pay, which began on Friday.
Tensions have risen between the government and public workers, increasing fears that South Africa's economy, the biggest on the continent, will be damaged by the protests.
The government has threatened to fire striking workers.
Fikile Slovo Majola, the general secretary of the National Education Health and Allied Workers Union, said the government's comments would not help to reach a resolution.
"The Department of Health's threats to fire nurses is only going to put negotiations in jeopardy," he told Reuters.
The strike actions have been co-ordinated by COSATU, South Africa's federation of trade unions and an important partner in a political alliance with the ruling African National Congress.
COSATU's affiliated unions make up about 60 per cent of public service employees, including doctors, nurses, police and teachers. So far, the strike has mainly hit the health sector.
The government had earlier offered pay rises of six per cent, but union leaders have said they will not end the strikes until the government agrees to double its pay rise offer to 12 per cent.
While South Africa's economy is booming, civil servants complain that they have not had a pay rise since one was granted to them to end a major public service strike in 2004.
The government, led by Thabo Mbeki, the South African president, says it is concerned a significant wage increases could further raise inflation in the country.
But the public reacted angrily when an official body recommended Mbeki himself receive a 57 per cent pay rise.
Negotiations to end the strike and reach an agreement on pay resumed on Monday.