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Meanwhile the union which won its fight for binding regulations to protect mineworkers from the pandemic has said new rules don't go far enough and has warned of "a crisis of epic proportions".
Harmony said both people who tested positive were asymptomatic, had been isolated and were receiving medical care.
CEO Peter Steenkamp said Kalgold would only return to full production "once it is safe to do so".
The openpit gold mine in the North West province employs about 600 people and represents 3% of Harmony's total production.
"While mining at Kalgold has largely been suspended, the plant continues to operate and employees who have tested negative for COVID-19 have returned to work," Steenkamp said.
South Africa moved to level four restrictions this month, allowing openpit mines to resume at 100% capacity and underground mines at 50%.
Harmony also has nine underground mines in the country, plus operations in Papua New Guinea, and recently withdrew its FY20 production guidance of 1.4 million ounces, due to the impact of COVID-19 and continued uncertainty regarding when its South Africa mines would be allowed to return to full production.
South Africa this week introduced new rules to put binding regulations on mining companies to protect workers from the global pandemic.
However the Association of Mineworkers and Construction Union, which pushed for the minimum standards, has now demanded every worker be tested not just screened, given the number of asymptomatic cases.
It made the call on Monday, after Impala Platinum closed its Marula operation on the weekend as it reported 19 asymptomatic COVID-19 cases "at and around" the operation in Limpopo province.
"The only way to ensure the safety of mineworkers, as well as the sustainability of the industry, is to upscale to universal testing," AMCU president Joseph Mathunjwa said.
"If we fail to do this, we will face a crisis of epic proportions."
The Minerals Council South Africa's tally of confirmed COVID-19 cases in the industry remained at 41 yesterday, from 1,517 employees tested and 172,674 screened.