During Tuesday’s visit, an angry mob, which blamed the government for the deaths, insulted the police and mines ministers and ordered them to leave.
Police said that more than 1,500 miners came to the surface before the rescue operation began.
However, others remained underground either because they feared arrest or were forced to stay there by the gangs that control the mine.
Many mines in South Africa have been abandoned over the past three decades by companies that did not find them economically viable.
The mines have been taken over by gangs, often ex-employees, who sell the minerals they find on the black market.
This includes a mine in Stillfontein, about 145 km (90 miles) southwest of the country’s largest city, Johannesburg, which has been the focus of government efforts to crack down on the illegal industry.