Shares in the company, majority-owned by ArcelorMittal, dropped more than 10% after it said previous initiatives to reduce costs had proved insufficient and so it was contemplating a "large-scale" restructuring.
"More significant measures have become necessary, including the review of staffing levels, together with other interventions," it said in a statement.
"It is anticipated that in excess of 2,000 positions (full time equivalents) may be affected," it continued, adding the final number was subject to formal consultation.
The company employed around 8,850 people in 2018, according to its annual report for that year.
ArcelorMittal South Africa, which has for some time complained about cheap imports eating into its business, said ongoing challenges in the steel industry as well as a weak South African economy had hit its performance.
These factors had been exacerbated by high costs for power, rail and port use, as well as raw materials, it said.
The company said it expected headline results to fall by at least 650 million rand (£37 million) in the first half of its financial year, plunging it deep into a loss compared with earnings of 54 million rand in the same period last year.
It said it would release a further trading statement once it has more certainty on headline earnings per share, the main profit measure in South Africa that strips out certain one-off items, and loss per share.
At 0845 GMT, the company's shares were down 9.3% at 31.4 rand, off an earlier low of 28.7 rand.
It also said, however, that its overall first-half loss for the period was expected to improve by at least 700 million rand, resulting in an improvement in loss per share.
(Reporting by Emma Rumney, Editing by Louise Heavens and Mark Potter)