Icahn Enterprises offered Monday to buy all outstanding Pep Boys stock for $18.50 a share in cash, which would value the auto parts company at about $1 billion. The company said its board determined Icahn's offer was superior to a bid from Bridgestone that it had previously accepted.
Icahn and Bridgestone had engaged in a bidding war in recent weeks. Monday's proposal was the third from Icahn, who already holds a more-than-10 percent stake in Pep Boys.
Icahn said he would not raise his bid higher than $18.50 per share unless Pep Boys increased Bridgestone's termination fee of $39.5 million.
Bridgestone first said it would acquire Pep Boys in late October.
Pep Boys shares fell nearly 3 percent in extended trading Tuesday.
— Reuters contributed to this report.