DALLAS — Southwest Airlines Co. launched a fare sale on Tuesday for travel this winter, and rival airlines began matching the prices on many routes.

Southwest said it was offering round trips starting at $98 for flights under 500 miles each way, with longer round trips costing up to $298. It said that the prices were good until midnight Thursday night and also applied to its AirTran Airways subsidiary.

The company said that sale prices applied to a limited number of seats, covered only nonstop flights, weren’t available on Fridays or Sundays, and carried other restrictions. The offer covered travel between Dec. 4 and Dec. 18, and again between Jan. 7 and Feb. 12.

By Tuesday afternoon, United, Delta, American and US Airways began offering similar prices and restrictions on most domestic routes that they share with Southwest, according to Rick Seaney, CEO of fare-tracking website FareCompare.com.

Separately, Travelocity.com said Tuesday that the average domestic airfare for Thanksgiving travel was $415 including taxes, an increase of 7 percent from last year. The online travel agency said many popular routes were cheaper than $415, however. It advised travelers to book flights before Nov. 10, when it expects fares to start rising sharply.