"I do not think we have lost control of the situation at the mines. The violence and intimidation has left our members feeling unsafe and not going to work," the union's health and safety chair Peter Bailey said.
He said Lonmin's Marikana mine had 27 000 employees and that "only" 3 000 of them were striking at the Wonderkop squatter camp.
Earlier on Friday, a fourth mine, Aquarius Platinum in Rustenburg shut down due to a strike.
NUM's national executive committee met in Johannesburg to discuss the situation at the mines.
Deputy president Kgalema Motlanthe was part of the meeting.
NUM has instructed its members to stay home, said Bailey.
"Our members' safety cannot be guaranteed so we urged them to stay home."
Secretary general Frans Baleni said NUM members wanted to arm themselves for self-protection against the violence at Lonmin.
"Our members want to arm and protect themselves because intimidation and violence has reached alarming rates."
At least 35 people have been killed in Marikana since the violent protest started last month. Ten had been killed in a week leading to the protest.
This week, NUM shop steward Godfrey Mthiti was found dead at the Wonderkop informal settlement.
Baleni said Mthiti was killed for voicing a different view.
"He was killed for mainly indicating to his colleagues that the strike had gone on for too long... that they should go back to work so that negotiations can continue smoothly."
The executive committee proposed that a commission of inquiry into the mine industry be established, said Baleni.
He said the strike was led by ring leaders who do not work at any of the mining companies.
'Most of them were dismissed during an illegal strike back in 2008. They are doing everything they can get their jobs back."
The union's deputy president Piet Matosa said expelled ANCYL leader Julius Malema was a "dangerous fellow."
Malema has never worked anywhere in his life and has failed to unite the ANCYL, said Matosa.
"He only wants to see people suffering and without jobs... hence we continue to warn miners against this dangerous fellow."
Malema has been visiting miners since the Lonmin Marikana strike commenced last month.
Last week, he told striking miners at Goldfields near Carletonville not to return to work until their demands were met.
He also called on a national strike to take place once a week every month.