Amcu was expected to hand over a memorandum at Lonmin offices in Melrose Arch, Johannesburg.
The marches would expand to Parliament after the Easter holidays if the union’s demands were not met.
Amcu-affiliated members working in the platinum mining sector have been on strike for over two months, demanding a minimum wage of R12,500 a month.
On March 27, Amcu president Joseph Mathunjwa said the union had given Amplats until April 5 to respond to the demands.
The labour union marched to Impala Platinum’s head office in Illovo, Johannesburg, to hand a memorandum to the company on March 27.
A meeting was held at Commission for Conciliation, Mediation, and Arbitration (CCMA) on Monday, attended by the producers and the Association of Mineworkers and Construction Union (Amcu).
On Tuesday the CCMA said the ongoing strike in the platinum sector would continue following a meeting between employers, Amcu, and the CCMA.
Lonmin spokeswoman Sue Vey said progress to settle the dispute and end the strike could only be made if Amcu moved towards the “settlement zone of nine percent”.
Impala Platinum spokesman Johan Theron said in a statement the parties were still far apart following the meeting.
Amcu members at Lonmin, Anglo American Platinum, and Impala Platinum downed tools on January 23 to push for a basic monthly salary of R12,500. They had so far rejected a wage increase of up to nine percent.
The companies, in turn, rejected Amcu’s revised demand that the R12,500 could be achieved over four years.
Last week, mining bosses said the strike had caused irreparable harm, and caused loss of an estimated R10 billion in revenue.