While noting those who died in the fire were on the Harmony Gold property at Welkom in Free State province illegally, Mining Minister Susan Shabangu said she was saddened and offered her condolences to their families, Independent Online reported.
"These are human lives that have been lost; children have been orphaned and women have been widowed. I would therefore like to extend sympathies to the families of the bereaved," she said in a statement.
Shabangu was expected to visit the site Wednesday.
The victims' bodies were brought to the surface during the weekend.
The Web site iAfrica.com reported the company, the third-largest gold producer in South Africa, said 294 illegal miners arrested in the past two weeks would be prosecuted.
Harmony Chief Executive Officer Graham Briggs said steps were being taken to tighten security at mine shaft heads, with daily search operations underground and improved access control measures.
Harmony said it would not send its employees into the abandoned sections of the mine because of the danger.
It wasn't known whether there were more victims still underground, iAfrica.com said.