The threat was made by representatives of hundreds of protesting workers who marched to Lonmin's Karee mine, from Marikana on Wednesday.
The five representatives told manager Jan Thirion that management had Wednesday and Thursday to close the mine's K3 shaft or they would end up dead and the mine would be burnt down. The shaft is where most of the mine's operations take place.
On August 16, police fired on a group of protesting workers near the mine, killing 34 and wounding 78.
Another 10 people were killed earlier that week, including two policemen and two security guards.
Thiroun, who arrived at the gate escorted by two heavily armed bodyguards on Wednesday afternoon, told the workers' representatives to go back to the negotiating table and sign the peace accord.
"Violence doesn't solve anything. It is not in everyone's interest."
When the marchers arrived at the mine, police took up position about 500 metres from an entrance gate, and kept a close watch. Two helicopters circled overhead.
Workers have been on strike for the past three weeks, demanding a monthly salary of R12 500.
On Wednesday, the miners started marching the more than 5km from Lonmin's mine in Marikana to the mine in Karee around 10am in an apparent attempt to stop their colleagues from working there.
The marchers carried knobkerries, sticks and iron rods and as they marched, sang: "We died because of [President Jacob] Zuma. [Bantu] Holomisa please come and rescue us."
They also carried placards bearing pictures of their dead colleagues.
Police were unable to prevent the marchers from entering Marikana.
‘Viva R125, viva’
Five Nyala armoured personnel carriers parked at the town's entrance in an attempt to divert the march, but the crowd pushed its way around the vehicles and continued to the Karee mine.
As the miners passed the Karee West informal settlement, next to the mine, residents cheered in support.
Men whistled and women ululated as the group passed by. They also shouted: "Viva R12 500, viva".
On Tuesday, about 200 mineworkers met at the Karee mine's shaft 30, and tried to get their colleagues to stop working. Another march was then planned for Wednesday morning.
Police in armoured vehicles also kept an eye on the Nkaneng informal settlement at Wonderkop, near the Marikana mine.
Talks between worker representatives, unions, the labour department and management were expected to resume on Wednesday in Rustenburg.