The nation's airlines continued to announce thousands of employe layoffs yesterday as a result of flight cutbacks caused by the three-week-old air traffic controllers strike.

Trans World Airlines and Northwest Airlines yesterday said they will cut employment by 2,700 workers beginning next month largely because of the strike. TWA said it will reduce the ranks of its 32,500 employes by 2,200 because of normal seasonal adjustments for the slower fall season in addition to the strike.

The company will furlough 150 pilots, 800 flight attendants, 700 machinists and 200 other workers in agent and clerical positions. The termination of another 350 management positions, announced in May, will be completed by the end of the year.

About 1,000 of the furloughs would have occurred without the strike as part of seasonal reductions at the end of the peak summer season, TWA said.

Northwest Airlines said it will reduce its job force by 500 because of the strike. The airline will end part-time jobs for the summer peak season earlier than usual, and it has obtained leaves of absence from some employes.

Meanwhile, the Federal Aviation Administration said yesterday that it will extend for the next seven months its current curtailed flight schedule, allowing only between 75 percent and 86 percent of normal volume in the air. The plan, originally set in motion immediately after the strike, will allow the airline industry to restore some predictability to the uncertain flight schedules caused by the strike that have contributed to a drop in passengers.

So far the FAA has allowed only one-half of scheduled flights at 22 major airports during peak morning and late afternoon flying times. The restrictions average out to a 25 percent cutback in flights. The FAA said that later it will consider increasing the number of flights during holidays to accommodate the usual heavy volume of traffic.

Many airlines said they will use larger and more-fuel-efficient aircraft to accommodate more passengers with fewer flights.

Last Friday Eastern Airlines said it was reducing its work force by 3,000, and half of those reductions were attributed to the strike, according to Eastern spokeswoman Ida Roberts. About 1,000 employes usually are let go at the end of the busy summer season, Roberts said.

About 500 of those workers accepted voluntary leaves of absence, allowing them to keep some benefits for up to six months without receiving pay.