Populist firebrand politician Julius Malema warned he would make mines in South Africa "ungovernable" after being booted out of the African National Congress in May.
After the mass shooting at the Lonmin mine, he accused Zuma of presiding over a "massacre of the people of South Africa".
"How can he call on people to mourn those he has killed? He must step down," he said.
The authorities came in for heavy criticism of their handling of the shooting and its aftermath. Up to 270 miners were arrested and initially charged with murder after police opened fire on workers at Lonmin PLC's platinum mine.
The charges were brought under an apartheid-era collective responsibility law termed the "common purpose doctrine".
It was designed to silence dissent among the black population by making whole groups responsible for the actions of individuals.