Its workers have been given until March 7 to resolve their complaints or face retrenchment, according to Business Day.
Harmony CEO Graham Briggs has warned in an open letter that roleplayers had 60 days to save the mine.
The letter said murder, violence, intimidation and damage to mine property prompted the decision to suspend operations at the mine near Carletonville.
He told Business Day that no company could operate in such an environment.
"We can't continue like this. Yes, it is as stark as that," said Briggs.
A meeting between unions and mine management was scheduled to happen on Thursday.
"The tables have turned. It is us, the company, which has demands on the table now, not the unions," said Briggs.
"Our demands are that we respect the law, that we are peaceful and respect the Mine Health and Safety Act."
Unprotected labour action at the mine in October and December caused huge production losses.
On Monday another mining company, Anglo American Platinum, warned investors it might have plunged into a heavy loss last year, as a result of labour unrest.
In a profit warning – filed with the Johannesburg Stock Exchange – Amplats said that 2012 earnings would probably show a loss of 491 to 628 cents per share, down from a profit of 1 365 cents per share in 2011, reported Agence France-Presse. – Sapa