United Airlines yesterday reversed itself and asked the Civil Aeronautics Board for permission to extend its discount "Freedom Fares" through next May.

Last week United said it would drop general application of the 15 and 20 percent discount fares beginning Sept. 15 and would keep them only on selected routes which are served by airlines retaining a similar discount fare.

Yesterday, United proposed to continue the fare system-wide and to add a new Freedom Fare discount on night flights.

Freedom fares offer discounts of 20 percent on flights Monday through Thursday and 15 percent on Friday through Sunday for travelers who buy tickets at least seven days in advance and don't return from their destinations until the first Sunday after departure, up to 45 days. The fares had been scheduled to expire on Sept. 14.

United also said it would offer new Freedom Fare discounts of 30 percent on most midweek night flights departing between 9:00 p.m. and 6:59 a.m. and 25 percent on weekends. The new night fares will start Sept. 25 assuming CAB approval.

United will also retain a full range of discount fares including the Super Saver, Super Coach, and Nightcoach discount offering price reductions of up to 50 percent depending on the route and the time of day.

Up to 35 percent of United's states are available with Super Saver and Freedom Fares, while there is no seat limitation on night coaches.

In other developments:

Trans World Airlines announced it would consolidate its fare offerings in a simplified structure like the one American Airlines proposed last week.

Western Airlines made a bid to increase its share of the California intrastate air travel market by holding the line on fares - and not matching the higher fares recently won by two California instrastate carriers - and by instituting a series of discount fares as well.

Western said its action will make its regular Los Angeles-San Francisco fare $28.10 one-way, compared with the competition's $32. Western will also offer a "proposition 13" fare at a roundtrip price of $26 on a seven-day advance purchase basis.

Icelandic Airlines announced it will adopt a single winter fare of $149.50 each way across the Atlantic on Sept. 15. The price is $30 below Icelandic's current lowest fare on its route between New York and Luxembourg. Those who buy a round-trip ticket in the United States at the winter rate may return on a summer fligh because the ticket will be good for a year.