Leaders of striking miners say the offer falls far below their demands for a minimum salary of 12,500 rand ($1,560).
When the offer was announced miners in the fifth week of a no work-no pay strike groaned in disappointment.
One shouted that Lonmin can shut down its mine if it does not meet their demand.
The strike has spread to the world's largest platinum mine, Anglo American Platinum, and has also stopped work at a gold mine.
Miners are calling on co-workers to shut down mines nation-wide raising fears for the future of South Africa's biggest industry.