"This phenomenon started at Impala Platinum, where workers were intimidated and attacked," general secretary Frans Baleni told reporters in Rustenburg.
"We are still awaiting the successful prosecution of those who committed the same acts at Impala."
A tenth body has been discovered at Lonmin's troubled Marikana mine in the North West, police said on Tuesday.
"We were notified of a body found in the bushes. The total figure now stands at 10. We don't know who the man was and how he died," said Captain Dennis Adriao.
A Sapa reporter who was on the scene said the body was lying, face upwards, 100m away from a hilltop where workers gathered earlier on Tuesday.
The man was wearing khaki clothes.
Nine other people - two police officers, two security guards, three protesters and two other men - had been killed the past few days at Lonmin's Marikana mine in violence that started on Friday. Members of the NUM and the Association of Mineworkers and Construction Union (Amcu), were reportedly fighting for control of local mines.
Baleni accused Lonmin of negotiating with rock drill operators outside the bargaining council. The company had offered the drillers extra money to retain their skills, he said.
"That resulted in other people approaching the workers, promising to negotiate more money for them. The company's actions undermined bargaining structures."
He said Amcu was the "smaller union" and was recruiting members from "mountain tops".
"The police did not take our advice regarding this phenomenon, despite what had happened at Impala."
Baleni said the union's membership in the country's platinum belt was not under threat.
Amcu's claim that the NUM was about to lose recognition status was "hogwash", Baleni said.
"We have over 60% representation at Lonmin [JSE:LON]. We are the majority union and are growing."
Solidarity and Ceppawu are the other two unions at Lonmin.