Police said the workers were arrested as they staged the demonstration in Salem, about 160 km from here, without permission.
The workers threatened to intensify their agitation if the government went ahead with its 'decision'.
According to trade union sources, the plant which had many ancillary units employed nearly 2,000 workers.
AITUC sources claimed that as part of its privatisation plan, the Centre had decided to float a global tender.
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In April this year, Chief Minister K Palanisamy had opposed the move to privatise the SSP, saying such a proposal would cause "considerable unrest" amongst the people, particularly amongst those whose lands were acquired.
In a letter to Prime Minister Narendra Modi, he had said the plant had acquired a global reputation for its high quality steel and "is an iconic symbol" for Tamil Nadu.
The Centre had in March last approved outright sale of state-owned SAIL's three special steel units, including Salem and Alloy Steel plants.