The rally - and indeed the announced job cuts - come just days after the anniversary of police shooting dead 34 miners at the nearby Marikana mine.
"The workers are not happy with the job losses," Joseph Mathunjwa, president of the Association of Mineworkers and Construction Union (AMCU), told AFP.
"Job losses should come as a last resort," he said.
AMCU officials are due to meet with management on Wednesday to discuss options.
Amplats, the world's top platinum producer, posted a net loss of R1.468 billion in 2012, but last month it reported it had recorded profits of R1.2 billion in the first half of 2013.
Chris Griffith, Chief Executive Officer of Anglo American Platinum, said, "We are at a critical stage of the process and this restructuring will be a crucial step to enable us to return to profitability and to focus capital allocations on our mines that are best placed to sustain the business and create employment opportunities over the long term."
"A month`s notice period for affected employees will commence on 1 September. We are very aware of the impact this process has on our employees and we are working hard to finalise the details of our Social Impact Mitigation Plan aimed at minimising the impact on employees and affected communities."
"The implementation of our proposals will help us create stability for the business and we look forward to working constructively with all our key stakeholders during this time for the benefit of all. Once we have restructured the business, we expect to be in a better position to provide more secure employment for our employees and add the much needed value to all our key stakeholders."
National Union of Mineworkers spokesman Lesiba Seshoka was "shocked" by the news.
"We are shocked. Our agreement with Amplats was to cut 3,000 jobs and those jobs would not be forced retrenchments but voluntary severance packages. This agreement was reached a week ago," he said.
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