Icahn said he will stick with his original bid price of $15 a share for the tender offer, despite the company terming the offer as low.
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"After attempting to work with the board, we are launching this tender offer so that shareholders can decide for themselves what they wish to do with their company," Icahn said in a statement.
On Monday, Commercial Metals had urged its shareholders to vote against Icahn's bid, which requires stockholder approval to authorize, adopt or amend any rights plan.
The company had adopted a shareholders' rights plan in July to prevent Icahn from increasing his near-10 percent stake in the company.
Shares of the company were trading marginally up at $14.18 on Tuesday on the New York Stock Exchange.
They had lost about a third of their value this year before Icahn unveiled his bid last week. The stock has failed to touch the $15 offer price so far.