Hertz Global Holdings Inc fired the latest salvo in a 13-month-long battle for Dollar Thrifty Automotive Group Inc , offering nearly $2.1 billion as it looks to form the No. 2 U.S. car rental firm and bump a stalled bid from Avis Budget Group Inc .

Hertz's latest bid is at a 3 percent premium to Dollar Thrifty's closing price on Friday and is worth over 30 percent more than what it offered in September last year -- a bid that was later rejected by Dollar Thrifty shareholders.

Demand for car rentals is rebounding as the travel and tourism business recovers from the recession, and Hertz has been looking to boost its presence in the $10 billion off-airport market and expand into new regions and sectors.

Hertz is offering $72 a share for Dollar Thrifty, or $57.60 in cash and 0.8546 Hertz share. Its previous offer consisted of $43.60 in cash and 0.6366 Hertz share.

Dollar Thrifty shares, which had gained 79 percent since the first Hertz approach in April of last year, jumped over 13 percent and hit a record high on Monday, well above Hertz's offer and indicating investors expect the bidding could go higher.

We'd like to see it higher ... a friendly deal, said Mike Shannon at Westchester Capital Management, the third-biggest investor in Dollar Thrifty with a 7.18 percent stake. If Dollar Thrifty were to sit down with Hertz, the offer could be 10 percent higher.

In September, Hertz walked away from efforts to acquire Dollar Thrifty after shareholders rejected its offer, leaving rival Avis as the likely winner in a long-running bidding war for the company. Avis and Dollar Thrifty never signed a merger agreement, choosing to get antitrust clearance first.

But that protracted approval process, along with improving conditions in the economy and the car rental industry, have given Hertz renewed confidence to take another swing at Dollar Thrifty now, people close to Hertz said.

Hertz said it has begun talks with the Federal Trade Commission, which works with the Justice Department to enforce antitrust law, about the transaction. It expects to close the transaction in the third quarter.

AVIS TO RETURN?

Hertz, the second-largest player in the U.S. car rental market, could have a clearer path to a regulatory green light as it focuses more on higher-priced car rentals and has less overlap with Dollar Thrifty's low-cost offerings, analysts have said.

On a conference call, Hertz Chief Executive Officer Mark Frissora said he wouldn't be surprised if Avis came back into the bidding: But we're not in a position here to go back and forth on bidding until there's a resolution of the FTC issue, he said.

Avis Budget declined to comment. Dollar Thrifty could not be immediately reached for comment.

The driving interest here is deal certainty, said Neil Abrams at Abrams Consulting Group. There's likely to be a growing belief that there is more certainly on a Hertz deal.

Dollar Thrifty and Avis have been pursuing antitrust clearance since October, when Avis made a cash-and-stock offer for Dollar Thrifty worth $1.67 billion based on Avis' Friday close.

Avis Budget has been unable to produce a viable antitrust remedy, despite an entire year of discussions with the FTC with no end in sight, Hertz CEO Frissora said in a statement.

Consolidation in the U.S. car rental market has been rapid, leaving four major rivals -- Hertz, Avis, Dollar Thrifty and privately held Enterprise Rent a Car.

Enterprise, which also owns Alamo and National Car Rental, is by far the biggest player and is twice the size of second-ranked Hertz and No. 3 Avis. Dollar Thrifty ranks fourth, according to data from industry publication Auto Rental News.

More recently, the successful trading debut of Zipcar Inc highlights the attraction for investors of the small, but growing, U.S. car-sharing industry.

ANTITRUST CONCERNS

Antitrust concerns have been key in the battle for Dollar Thrifty, which last year rejected Avis' advances saying it would be tough to win antitrust approval.

Hertz does have a low-cost offering through its Advantage brand -- but is already in the process of selling it.

Barclays Plc's Barclays Capital, Lazard , Bank of America Corp's Merrill Lynch and Deutsche Bank Securities are acting as financial advisers to Hertz. Citigroup and Morgan Stanley are advisers to Avis. Dollar Thrifty are being advised by JPMorgan Chase and Goldman Sachs Group .

Hertz shares hit a 41-month high earlier this month and Dollar Thrifty's stock price has increased 14-fold in 2 years. On Nasdaq, Avis shares are up 18 percent this year.

At midday, Hertz shares dipped 0.7 percent to $16.74, while Avis gained 0.2 percent to $18.44. Dollar Thrifty shares were up 13 percent to $78.75. They touched $79.13 earlier.

(Additional reporting by Bijoy Koyitty, Michael Erman in New York and Diane Bartz in Washington; Editing by Ian Geoghegan and Gerald E. McCormick)