Hertz Global Holdings Inc., the largest publicly traded rental-car company, offered to buy Dollar Thrifty Automotive Group Inc. for $2.24 billion in cash and stock, countering a bid by competitor Avis Budget Group Inc.

Hertz offered $72 a share, 24 percent more than Avis’ offer, Bloomberg reported today.

Hertz aims to thwart the planned combination of Avis and Dollar Thrifty after having an earlier offer rejected. Since then, Avis and Dollar Thrifty have been seeking U.S. Federal Trade Commission (FTC) approval for a deal that would combine the third- and fourth-largest U.S. rental car companies, Bloomberg said.

Hertz’s offer, which isn’t subject to financing conditions, consists of $57.60 in cash and 0.8546 Hertz share per share of Dollar Thrifty. Including options and equity awards, Hertz said Dollar Thrifty has 31.2 million shares outstanding.

The rental-car company, which has begun the process of selling its Advantage brand to facilitate FTC approval, has started discussions with the regulator, Hertz said.

Investors in Dollar Thrifty rejected a $1.44 billion offer from Hertz, the largest worldwide airport car-rental brand, on Sept. 30, 2010, providing an opening for Avis to buy the company. At the time, Hertz said the offer was its “best and final.” The winning bidder would become the second-largest U.S. auto-rental chain by revenue, trailing only closely held Enterprise.

Avis offered $45.79 and 0.6543 of its shares for each share of Dollar Thrifty and, in October 2010, agreed to delay an exchange offer while the two companies began working toward regulatory approval. Avis also offered a $20 million breakup fee that Dollar Thrifty had requested.