Icahn earlier this year put Sugar Land, Texas-based CVR in play with an offer of $30 per share, with a contingency that would give current investors an additional gain should he flip the company within nine months. CVR rejected that offer as inadequate and enacted a poison pill, and the two sides in the months since have been fighting an increasingly testy battle for control of the company.

The investor, who owns about 14.5% of the company, earlier this month announced that 55% of shares outstanding had tendered in favor of his offering, raising pressure on CVR's board to open talks. CVR on Thursday said it would drop its poison pill and allow Icahn to complete his tender offer if he obtains a majority of shares.

CVR said its board has not changed its recommendation against the tender, and continues to believe that the company's "potential long-term value exceeds $30 per share." In dropping the poison pill the company will force Icahn to show whether he really wants to buy CVR, or if he only launched his tender in hopes of forcing the company to conduct an auction.

Icahn in a statement said he would be mailing a supplement to the tender to CVR shareholders in the coming days, adding that the tender would expire ten business days after the mailing. Assuming he wins control of the company Icahn said he would immediately have CVR engage in a 60-day auction process, pledging to support any bid of at least $35 per share.

"We agree with the board that the company's potential long-term value exceeds $30 per share," Icahn said. "However, we also believe that if the company cannot be sold in the next two months there are major risks to earnings in the short and intermediate term."

Icahn has warned that if refining margins narrow in the months to come, as he expects, smaller refiners like CVR will be at risk.