NEW YORK— Priceline.com said on Oct. 2 it expects third-quarter revenues to come in toward the higher end of its revised range of $280 million to $300 million as demand for its services was recovering faster than expected after the attacks on the United States. The name-your-own-price Internet company, whose business includes the sale of airline tickets and booking hotel reservations, had warned on Sept. 21 its quarterly revenues would be lower than expected because of the Sept. 11 attacks on the World Trade Center and the Pentagon. A year earlier, Priceline posted revenues of $341 million. Wall Street analysts, on average, had expected the Norwalk,CT-based company to post revenues of $287 million in the third quarter, according to Thomson Financial/First Call. Pricelines shares have taken a beating as travel bookings have plummeted in the wake of the attacks. In after-hours trading on Oct. 2, Priceline shares were last at $4.05 after gaining $.09 to close at $3.67 — still off sharply from its pre-attacks close of $6.06 on Sept. 10, but gaining support from recent stock purchases by investors, including Chief Executive and Chairman Richard Braddock and Hong Kong tycoon Li Ka-Shing. On Sept. 21, Priceline had said bookings on Sept. 17 were 40% lower than they were a week earlier— the day before the attacks. However, the company said in a statement Tuesday that total unique offers for its services for the week ended Oct. 1 have recovered to 94% and total units sold have recovered to 82% of the levels before the attacks.