Impala Platinum Holdings, also known as Implats, said that 63 of the 2,205 miners who started the protest Monday had come to the surface during the night.
The company called the action an "illegal underground protest" and warned it will "address those employees who engage in illegal conduct and criminal acts in a decisive way."
All operations at the mine, northwest of Johannesburg, have been halted while talks are held with the workers and unions.
National Union of Mineworkers (NUM) officials "managed to engage workers last night and started the process to address their concerns with management," a company spokesman told AFP.
"Hopefully we can respond today through the NUM and agree a process to return all workers to the surface and resolve issues in a normal constructive engagement," he added.
South Africa has seen a growing number of underground protests by miners.
"Illegal underground protests and copycat illegal actions... have become more prevalent in recent months," Implats said.
More than 100 gold miners spent nearly three days underground in Springs near Johannesburg in October as rival unions battled for control.
Another 440 staged a protest in another gold mine this month while 250 platinum workers demanding better wages occupied a shaft for three days at the same time.
Mining employs hundreds of thousands of people in South Africa -- the biggest exporter of platinum and a major exporter of gold, diamonds, coal and other raw materials.
South African Miners Begin Second Day of Protest
FILE - Two miners (2nd R and 4th R) look on after they resurfaced, because of medical conditions, from the underground protest at the Bafokeng Rasimone Platinum Mine near Rustenburg on December 19, 2023.
RUSTENBURG, South Africa - More than 2,000 workers were occupying a South African platinum mine for a second day Tuesday as the owners upped the pressure to end one of the country's biggest mine protests in years.