“No matter what the motives of the perpetrators, the police will be doing everything possible to arrest them,” Mthethwa said in a statement.
Two mineworkers were killed at the weekend and another one on Monday.
“The protection of those involved in the labour disputes in the North West is a matter that government takes extremely seriously,” Mthethwa said.
Workers affiliated to the Association of Mineworkers and Construction Union (Amcu) in the platinum belt have been on strike since January 23 demanding a salary of R12,500 a month.
Mthethwa said policing would be stepped up on Wednesday when some striking mineworkers would return to work.
“There will be increased patrols along the routes that workers use to get to the mines and police vehicles will escort buses carrying workers.”
Mthethwa said violence against people or property would not be tolerated.
Fears of friction between striking miners and those wishing to resume work arose when Amcu objected to employers approaching miners with their wage offer directly, in a bid to end the strike.
Platinum producers Impala Platinum, Anglo American Platinum, and Lonmin have called on Amcu to exercise responsible leadership.
“We recognise the right to strike as a fundamental right of employees, a right which has been respected throughout the dispute,” they said.
“But we have a responsibility to communicate directly with our employees… our employees wish to return to work, but have expressed a fear of continued intimidation and violence.”
The companies urged Amcu to recognise and uphold the rights of those who wanted to work.
The National Union of Mineworkers’ (NUM) regional secretary Sydwell Dolokwana blamed Amcu members and employers for the three deaths.
“[They] intimidated our members who wanted to go to work on Monday. Our employer urged workers to report for duty on Monday and they could not even ensure the safety of the workers.”
Amcu could not be reached for comment on Monday afternoon.