Major airlines announced plans yesterday to cut back about two-thirds of all Washington-area scheduled flights on Monday if air traffic controllers strike.

A survey of 10 airlines that fly into Washington shows that, of their 207 regularly scheduled daily flights, only 67 will be operating if the Federal Aviation Administration suspends regular flight operations in response to a strike. The cutbacks will take place at all three major Washington airports -- National, Dulles and Baltimore-Washington International.

Among those affected will be the popular Eastern Airlines shuttle to New York City, which will be suspended and replaced by two scheduled flights a day to LaGuardia Airport; United Airlines, which will cut service from 28 flights to 16 at National and Dulles; and Delta, which will slash its normal 16 departures daily from National Airport to one flight to Atlanta.

The possible strike kept airline executives at round-the-clock meetings at their reservation operators racked up overtime answering confused inquiries.

"A lot of the burden on finding a seat on Monday is going to be with the passenger," said June Farrell of Eastern Airlines. "We're going to try to help them, but it's going to be difficult for both."

As the airlines prepared for cuts, other carriers prepared to handle extra passengers bumped from flights or who choose to switch their form of transportation.

Amtrak said it would add two extra cars to trains in the Northeast corridor and bus companies and rental car agencies readied themselves for the coming crush by calling up extra personnel and equipment.

Hertz, National and other rental car agencies said they will shift many of their cars to inner-city locations since they will have less business at their airport offices. "We except that with the strike, those originally destined for flights of less than 500 miles will opt to rent cars instead," said a Hertz spokesman.

William F. Bolger, postmaster general of the U.S. Postal Service, said yesterday that air mail will be affected if there is a strike. However, he said that priority air mail -- such as Express Mail, first-class letters and packages with first class postage -- would continue to be delivered by whatever air transportation is available if a strike materializes. All other mail that ordinarily is moved by air would be moved to ground transportation, he said.

Travel agencies throughout the Washington area said they were flooded with phone calls from clients wondering if they should postpone or cancel travel plans.

"We've been advising our clients to hold off their travel until late next week or try to get alternative arrangements on trains, buses or rented cars," said Ian Kerr, manager of the I Street NW office of Thomas Cook Travel, which makes domestic business travel arrangements for the American Medical Association, the Ford Motor Company, the Bell and Howell Satellite Group and the law firm of White and Case.

Beatrice Smith, sales manager at Rodgers Travel Bureau in Northwest, said 10 of her firm's 30 clients planning to fly to a convention in Omaha, Neb., next week here canceled and have been refunded their $300 fares.

At the Old Dominion Travel Service in Alexandria, several vacationers have stepped up their travel plans and will fly this weekend to beat the anticipated strike, according to Joy Collins, executive vice president of the firm. The agency is trying to arrange for other travelers to go by train from Washington to New York, where they will fly out of the country on foreign carriers not expected to be affected.

It was unclear yesterday whether the contingency flights would take effect on Monday, the day the strike is supposed to start, or on Tuesday.

A Braniff spokesman said there were reports that the FAA was planning a flow control plan for Monday, in which normally scheduled flights would be permitted but that they would hold airplanes on the ground until they got them cleared on the other end. Then the contingency schedule would begin on Tuesday.

Airlines were also hoping that the FAA would allow them to add more flights to their original lists as they see how well supervisors handle the flow of air traffic.

Because of the confusion about contingency flights to be offered by the various carriers, most airline reservation workers can only give callers information about their own contingency flights. This often requires calls to many airlines before getting reservations to the desired location. Also, most carriers report that baggage transfers between airlines will be suspended during the strike.

Carriers such as United and American have begun in essence double-booking passengers for flights starting Monday on both their regular flights and the contingency flights which the FAA will allow in the event of a strike.

Some carriers, like TWA and Northwest Orient, were reluctant to announce their specific contingency flights until Sunday.

One group that doesn't expect to be affected by the strike is the owners of the nation's 210,000 private aircraft. "More than 80 percent of all flying is normally done under visual flight rules, which do not require contact with controllers," said John Baker, president of the Aircraft Owners and Pilots Association.

"Face it," said a supervisor at Page Airways, which services corporate and private jets."Those corporate planes are going to fly."