There are 955 employees still underground and they are in a confined and safe area, said James Wellsted, spokesman for Sibanye-Stillwater.
The spokesman said the stranded miners are being supplied with water and food. "So everybody is fine at the moment. We are trying to restore power so we can start hoisting them to the surface," he said.
The company is reportedly using a generator to get the workers out of the mine. According to earlier reports, engineers had struggled with a software fault to get emergency generators to operate and re-start the lifts in the mine.
The spokesman said that buses have begun transporting rescued mine workers to their family members after the miners got a shower and some food.
Families of the miners have been keeping a vigil outside the mine shaft.
The South African Department of Mineral Resources tweeted that "currently all employees still underground are accounted for," and "the department's inspectors are on the site providing support and advice on the rescue operation."
Mineral Resources Minister Mosebenzi Zwane is scheduled to visit the mine Friday to determine what caused the miners to be trapped. The Beatrix mine, where the miners are trapped, is 290 km southwest of Johannesburg.
Mine safety is a serious concern in the country, which operates some of the world's deepest and most dangerous mines.
The Congress of South African Trade Unions (Cosatu) said it wants the government to investigate the cause of the tragedy.
"Our government needs to come to the party with some tangible enforcement mechanisms to ensure compliance with health and safety regulations and work to reduce mine accidents," Sizwe Pamla, Cosatu national spokesperson said.
They also called for the emergency services to double their efforts to rescue the trapped miners. Cosatu said mining companies should learn from past experiences to prevent an increase of mine fatalities.
"We need solid and sensible prevention mechanisms in place to help reduce and ultimately stop mining fatalities," Pamla said.