The halting of production at diamond, gold, platinum and other mines has sent prices of precious metals to record highs, weakening South Africa's currency, the rand.
The government of Thabo Mbeki has been criticised in recent years of underinvestment in power generation.
"Lights are going out on Mbeki and his regime," Donwald Pressly, a columnist, said in South Africa's Business Report on Sunday.
A meeting on Tuesday or Wednesday between mining firms, government officials and Eskom, the state energy company, would determine when and how mines could start production.
The mines are expected to resume work in a phased process so as not to compromise the power grid.
Eskom has warned mines that the crisis may last for up to four weeks.
"We are starting to emerge from a crisis that had the potential to undermine the viability of the South African gold industry," Mark Cutifani, the chief executive officer of AngloGold Ashanti, said in a statement on Monday.
AngloGold, the world's third biggest gold producer, said it anticipates power delivery by the end of this week.
Anglo American said its South African coal mines had resumed production on Monday following a series of weekend meetings with officials from Eskom.
Analysts fear the booming South African economy could slow down.
Mbeki's government has predicted the economy needs to grow by six per cent in order to fight poverty.
The crisis started after Eskom took down some power plants for routine maintenance and other power stations broke down.
Eskom plans to invest 300bn rand ($43bn) in power generation and infrastructure over the next five years, but has warned South Africa that there may be other power outages.
It currently produces over 90 per cent of its electricity from coal fired power plants.