NEW YORK — Hertz Global Holdings Inc. is raising the stakes in its pursuit of Dollar Thrifty Automotive Group Inc. in hopes of besting rival Avis Rent A Car System LLC’s efforts to acquire the Oklahoma-based car rental agency.

The two vehicle rental heavyweights have been in a virtual tug-of-war over Dollar Thrifty for a little more than a year, with both looking to snag the Tulsa company because its clientele is largely leisure travelers.

Hertz and Avis cater mostly to business travelers, so a Dollar Thrifty acquisition would give either one a broader client base.

Hertz sweetened the pot Monday. Its new proposal is worth $72 a share in cash and stock. This includes $57.60 in cash and 0.8546 share of its common stock. With 31.2 million fully diluted shares of Dollar Thrifty, the Hertz bid is worth about $2.25 billion and is 3.3 percent above Dollar Thrifty’s closing price last week.

Dollar Thrifty said in a statement its board will review Hertz’s bid and advised its stockholders not to take any action pending its review. Investors appeared to be betting that the bidding will go higher. Dollar Thrifty closed at $79.20 on Monday.

Hertz’s revised bid probably is likely meant to appeal to Dollar Thrifty’s stockholders, who stung Hertz in September when they rejected an offer that included $43.60 in cash and 0.6366 share of common stock. Dollar Thrifty’s board had recommended stockholders accept the deal.

At the time, industry experts speculated Dollar Thrifty shareholders favored a potential deal with Avis because it was more money than Hertz was offering. Avis had offered $45.79 a share in cash and 0.6543 share of Avis. At Friday’s price for Avis, that bid was worth $1.74 billion.

First Published May 10, 2011, 4:30 a.m.