An employee at the Khuseleka shaft, at the Rustenburg PGM operations, passed away about 2.30am due to a fall of ground incident.
Hours later, three colleagues at Beatrix's 3 Shaft died after a trackless mobile machinery incident at 10am, the company said.
It also confirmed a fatality earlier last week at the Beatrix gold mine due to a blasting incident.
Sibanye-Stillwater said the company had seen a perplexing, notable increase in fatalities with 18 lives lost so far in 2021.
"We are appalled by the loss of our employees' lives at our mines over the past year," Froneman said.
"While we cannot rectify the harm that has occurred, we will continue to support the families as best we can in their grief.
"The safety of employees is our primary concern and we will continue to strive for zero harm in the workplace."
South Africa's mining stakeholders met recently to address the industry's concerning safety regression, with fatalities on the rise since the record low of 51 in 2019.
Impala Platinum reported three fatalities from a mud rush incident at its Rustenburg 6 Shaft early last week.
CEO should resign: AMCU
The Association of Mineworkers and Construction Union has told local media it wanted Sibanye-Stillwater's Froneman to resign in the wake of the latest deaths.
AMCU head of organisational development Krister Janse Van Rensburg also said the government regulator should be split once again to purely focus on mining, not energy as well.
He said it had been one of the worst periods for mine fatalities.
"And the worst of the worst at the moment is Sibanye-Stillwater, it leads the pack in terms of killing the most workers this year," he told eNCA.
The AMCU and Sibanye-Stillater are also at loggerheads over unresolved wage talks, with strike action looming for the company's gold business after the miner could not reach agreement with four unions which banded together for negotiations.