Five diamond miners missing since Tuesday following a mudslide deep underground are presumed dead, South Africa's mining minister said on Friday after assessing rescue efforts.

Gwede Mantashe told a press conference that it was now a question of retrieving their bodies, public broadcaster the South African Broadcasting Corporation reported.

The miners were trapped more than 800 metres underground in the early hours of Tuesday morning, when there was a "mud-rush" at the Ekapa mine in the Northern Cape province.

Ekapa Minerals, the company that operates the mine, said all operations were stopped immediately after the incident and that rescue efforts were continuing.

"The time passed since the event is a major concern but there is no change in approach to the rescue activities and we are not giving up hope," Ekapa Minerals General Manager Howard Marsden said in a statement.

Mantashe said in a separate statement that an investigation would be conducted to find out what had happened.

South Africa's government and mining industry have been making efforts to reduce mine deaths and injuries, part of a campaign called "Zero Harm". Last year the country recorded its lowest-ever number of mine deaths, 41.

Ekapa Minerals said it had been briefing the families of the trapped miners, who held a vigil near the mine on Thursday night.

Kimberley, where the mine is located, was the site of a 19th-century diamond rush that lured fortune-seekers from the world over.

Diamond revenues funded the growth of South African industry and gold mines, which themselves helped finance colonial ruler Britain through two world wars.