"The safety and security of our employees is paramount and nobody will be asked to report for duty if the police consider them in danger of reprisals," CFO Simon Scott said in a statement.
Lonmin had initially ordered miners to return to work by Friday, then, after the shootings, changed the deadline to Monday, spokeswoman Sue Vey said.
"The final ultimatum provides RDOs with a last opportunity to return to work or face possible dismissal," the company said in a statement Sunday. "Employees could therefore be dismissed if they fail to heed the final ultimatum."
Strikers said they were not sure what to do. The company has not responded to their demands for the minimum wage to be increased from R5,500 ($688) to R12,500 ($1,560).
Last year after a similar dispute over labor representation stopped work at its nearby Karee mine, Lonmin fired all 9,000 workers. Then it asked them to reapply for their jobs and most were rehired.