Washington's National Airport and six other U.S. airports will be allowed no additional flights through next October, Federal Aviation Administration officials said yesterday.

The seven airports are among 22 major facilities whose operations have been restricted for the last six months because of the strike and firings of 11,438 federal air traffic controllers in August.

At a meeting attended by officials of all of the nation's largest airlines and many smaller ones, FAA official John R. Ryan announced that 15 of the airports whose activities have been restricted will be allowed varying increases in operations between April and October. The increases range from as few as 10 flights a day at New York's LaGuardia Airport to a total of 104 additional flights a day at Atlanta over the summer period. The increases generally will be allowed in increments, some for the April-May period, some for June and July, and some for August through October. At some airports, additional flights are restricted to certain hours.

Ryan, acting chief of the operations division of the FAA's Air Traffic Service, said that airports besides National that aren't slated for any increase in the number of flights during the peak summer travel season are Chicago's O'Hare, Cleveland, Dallas/Fort Worth, Houston, Minneapolis and St. Louis.

Ryan also said there will be phased increases in the allowable operations of 15 en-route traffic centers that guide air traffic between airports, and no increases in five others.

The Washington center at Leesburg will be allowed to handle up to 350 more flights a day in late April and May, 150 more in June and July, and another 150 from August through October. The increase in traffic allowed for the Washington center, combined with the level of flights at National frozen through October, means that any additional air service to the Washington area through the summer will have to go to Dulles International or Baltimore/Washington International airports.

The proposed increases will mean that the nationwide air system in August will be operating at about 90 percent of its pre-strike level, Ryan said. During the third week of January, the system was operating at nearly 83 percent of its pre-strike level, he said. However, air traffic normally is off in the winter so the winter comparison with last summer's traffic isn't as useful as a comparison with last winter's traffic would be. The FAA hasn't made that information available.

Raymond J. Van Vuren, director of the FAA's Air Traffic Service, told the airline officials that, by the end of this year, the air traffic system would be able to accommodate the same number of flights as it did before the strike, although there would be some restrictions at some places. By the end of 1983, the FAA expects to accommodate 100 percent of the traffic, including peak periods of flights, he said, adding, "We do see a lot of light at the end of this tunnel."

Van Vuren also provided an update on how the FAA is staffing the towers and centers. He said as of Dec. 1 there were 9,292 controllers, including supervisors, retrained staff and 759 military controllers. Since Aug. 3, the FAA has 2,925 new hires, inluding new trainees and some retirees brought back. Another 1,400, including 832 furloughed airline pilots, have been hired in flight data positions.

Although it has been relatively easy to redeploy controllers at towers, he said the en-route centers--with their different requirements--remain more difficult to staff.

Van Vuren also noted that the FAA had received 125,000 applications to fill the new controller positions; 60,000 of them came for tests. The FAA Training Academy is geared to take in up to 500 trainees a month, or 6,000 a year. After a wash-out rate of about 25 percent at the academy and 10 percent in the field, he said the FAA expects to get 3,700 controllers a year.

The FAA meeting was called to get carrier comments on how increases in flight allocations should be parceled out. Generally, the incumbent airlines wanted to see flights they lost reinstated before new airlines were given access to the airports. Representatives of new and prospective airlines wanted to assure that they could get access to the nation's airports in any allocation plan.