A limited fare war broke out yesterday among the airlines serving a number of markets including Washington, offering bargains for consumers who are fast on their feet.

America West, a Phoenix-based airline, started the fares rolling on Wednesday when it cut fares to a number of cities by 50 percent. Tickets have to be purchased by the end of the day Saturday, but they are good for travel until Jan. 5, 1992.

Several carriers quickly matched those fare cuts in markets in which they compete with America West. Then, yesterday, Trans World Airlines Inc. upped the ante by lowering fares in other markets.

In the face of those discounts, Northwest Airlines Inc. quickly decided not to impose a $15 surcharge on round-trip fares that had been scheduled to take effect today.

TWA's fare cuts apply to both normal and excursion fares for travel between two lists of cities. A passenger going from Boston; Baltimore; Chicago; the Iowa cities of Des Moines or Cedar Rapids; New York; Newark; Kansas City, Mo.; Minneapolis; Moline, Ill.; or Washington can get the half-priced fare to Los Angeles; Ontario, Calif.; Portland, Ore.; Phoenix; San Diego; Seattle; San Francisco; San Jose; Orange County, Calif.; or Tucson, or vice versa. Tickets can be purchased until midnight Sunday for travel this year.

Other airlines, including Northwest and American, are matching TWA's cuts in a limited way in many of the same markets. For instance, they are matching them only for excursion fares and only for travel until June 10.

The fare cuts are a short-term measure designed to raise cash during a traditionally slow period for the airlines now compounded by recession and fears related to the gulf war.

Underlining the industry's troubles, Midway Airlines Inc. of Chicago reported a whopping $86 million loss in last year's fourth quarter, and said it has temporarily suspended aircraft lease and loan payments. Midway said it has started talking with its creditors about restructuring its debt and expects to resume the payments in May. Analysts saw the talks as a possible attempt by Midway to avoid filing for federal bankruptcy protection.

Airlines are facing huge losses for this year's first quarter. The new fare initiatives probably won't increase those losses much, said Edward Starkman of PaineWebber Inc. "We're looking at a pretty big hole for the first quarter," he said. Delta spokesman Neil Monroe said, "It's not good for the industry. These types of prices don't reflect real costs."

This article was supplemented by news services reports.