Anglo American Platinum has asked the CCMA to facilitate discussions with unions about possible retrenchments.
"The first facilitation meeting [on] Friday was adjourned as the parties all agreed to a postponement," Commission for Conciliation, Mediation and Arbitration (CCMA) spokesperson Nersan Govender said in a statement on Friday.
This was to allow the unions to consult their members and finalise their delegations. The process would resume on January 30.
Amplats announced this week it planned to stop production at four of its shafts in Rustenburg, which could result in the loss of 14 000 jobs, and to sell a mine considered unsustainable.
As a result, Amplats workers refused to go underground on Tuesday. However, on Wednesday night they abandoned their illegal strike.
CCMA director Nerine Kahn said: "The CCMA remains committed to do whatever necessary to ensure the best possible outcome for all parties".
On Thursday, Amplats CEO Chris Griffith and Mineral Resources Minister Susan Shabangu met to discuss the company's restructuring plans. They agreed to meet again in the next 90 days.
"We welcome the opportunity for continuing engagement with minister Shabangu and her team," Griffith said in a statement on Friday.
"[The meeting was] to reach our shared objective of creating a sustainable, competitive, and profitable platinum business for the benefit of all stakeholders and for South Africa."
There would also be continuing discussions about the economic problems facing the platinum industry as a whole.
The company said updates would be provided in due course.
At a media briefing in Johannesburg on Monday, African National Congress secretary-general Gwede Mantashe said mining companies misrepresenting their intentions could have their licences revoked.
"Are companies giving nice plans to government so that they get the licence and once approved [they forget about it]?" Mantashe asked.
"If you misrepresent what your intentions are when you submit a plan, all parties have a right to revoke the licence." – Sapa