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

Hertz's latest bid is at a 3 percent premium to Dollar Thrifty's closing price on Friday and is almost double what it offered in April 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, comprising $57.60 in cash and 0.8546 Hertz shares.

Dollar Thrifty shares, which had gained 79 percent since the first Hertz approach, jumped more than 12 percent on Monday to a life-high and well above Hertz's offer, 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.

AVIS TO RETURN?

Shannon said it would be easier for Hertz to get antitrust approval than Avis.

On a conference call with analysts, Hertz CEO 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, referring to the U.S. Federal Trade Commission.

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 that is worth $1.67 billion based on Avis' Friday close.

That protracted approval process -- Avis already has a budget brand that competes with Dollar Thrifty -- has brought Hertz back into the fray.

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, 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, the market leader.

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 4th-ranked Dollar Thrifty, which last year rejected Avis' advances saying it would be tough to win antitrust approval.

Hertz, the second-largest in the market, is thought to have a clearer path to a regulatory green light as it focuses more on higher-priced car rentals and has little overlap with Dollar Thrifty's low-cost offerings.

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

Barclays Capital, Lazard, Bank of America Merrill Lynch and Deutsche Bank Securities are acting as financial advisers to Hertz.

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

On Monday, Hertz shares edged up 0.3 percent, while Avis dipped 0.3 percent.

(Reporting by A. Ananthalakshmi in Bangalore; additional reporting by Bijoy Koyitty; Editing Ian Geoghegan)

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