Earlier this week, security forces blocked deliveries of food and water to the miners in a bid to push them out of the mine.
The miners experienced “starvation and dehydration” and were forced to resurface, police say.
Individuals have been emerging from the mine, located in the northern town of Orkney, since Saturday, though hundreds are believed to remain in the shaft.
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On Sunday the national police boss encouraged security forces on the ground “not to back down” and to “ensure the rule of law is restored”, a statement from the force says.
The statement says that earlier this week, security forces “blocked communities in and around these abandoned mining shifts in Orkney from delivering food parcels, water and necessities to these illegal miners”.
The police reported on Saturday that 225 miners had resurfaced, but “hundreds if not a thousand” were thought to still be underground.
In an update on Sunday, the national force said an additional 340 had emerged from the mine and placed under arrest.
Thousands of illegal miners, known as “zama zamas” (“those who try their luck” in Zulu), operate in the mineral-rich country.
National Police Commissioner Lt Gen Shadrack Sibiya said that since December 2023, more than 13,690 suspects have been arrested across seven provinces.
“We have seized R5 million ($283,000; $220,000) in cash and uncut diamonds worth R32 million ($1.8m; £1.4m),” he said.
