The Federal Aviation Administration, saying that almost one in 10 scheduled airline flights was more than 15 minutes late last month, yesterday announced plans to hire 1,400 new air traffic controllers and ease some air traffic restrictions.

The FAA said delays were almost three times more frequent than during August a year ago.

The new statistics were released as FAA officials briefed airline executives gathered in Arlington in an attempt to reach a voluntary agreement to reduce overscheduling at six major airports. The scheduling of more takeoffs and landings than can be accommodated physically has contributed to delays.

If the airline executives cannot agree, the FAA has threatened to regulate access to the airports, a solution that would have considerable economic impact for a supposedly deregulated industry.

There were 44,372 flight delays nationwide in August, an increase of 276 percent over the same month a year earlier and the highest one-month total the agency has recorded since it began, in 1982, defining a delay as one that is 15 minutes or longer. Before then a flight was not counted as delayed until it was at least 30 minutes late in taking off or landing.

J.E. Murdoch, acting deputy FAA administrator, told airline executives that scheduling practices are not the only cause of delays, confirming something the airlines have been saying for months.

Also contributing are some restrictive air traffic control procedures, a shortage of experienced controllers, especially in the New York City area where delays are most persistent, a shortage of runways and gates at a few airports, and summer thunderstorms.

"The FAA has had to use delays as a mechanism to control" traffic, Murdoch said. The result this summer has been remarkable inaccuracy in published airline schedules, particularly in the Northeast.

Many of the FAA's controllers are relatively inexperienced replacements for the 11,400 illegally striking controllers President Reagan fired three years ago. Traffic levels are now higher than they were before the strike, although the FAA is using about 3,000 fewer controllers.

The 1,400 new controllers will build the total controller work force to about 14,300. This is 2,000 fewer than were employed before the strike but 900 more than are employed now. The FAA's air traffic control academy in Oklahoma City will increase instruction from one to two shifts in October to speed the training of new controllers.

John R. Ryan, manager of the FAA's operations division, said the agency is also planning to reduce inflight restrictions that contribute to delays and to permit 15-minute airborne holding patterns at several key airports.

Holding patterns present complex problems for controllers; the FAA has been reducing those problems by keeping planes on the ground until they could be guaranteed uninterrupted flights. The airlines prefer airborne holding because they want planes available to fill holes that might develop in a tightly scheduled system.

Another possibility is to standardize and reduce the spacing between planes en route. Currently this varies from region to region depending upon the experience of the controllers.

The voluntary scheduling meetings, requested by Eastern Air Lines and for which antitrust immunity was granted by the Civil Aeronautics Board, are expected to grind late into the nights and through the weekend as executives attempt to meet controversial FAA goals of scheduling fewer flights in peak periods.

Yesterday's meeting was to deal with overscheduling during peak hours at Atlanta's Hartsfield airport. Today's meeting concerns Denver's Stapleton airport and Friday's concerns Chicago's O'Hare. Saturday and Sunday are scheduled for the three New York-area airports: Newark, La Guardia and Kennedy.

Ryan said he would expect the airlines to limit the number of flights the airlines could schedule for each five-minute period. The total flights permitted differ depending on the airport, but the proposal is much more restrictive than 30-minute scheduling currently required for certain hours at O'Hare and La Guardia. The FAA has said it would enforce with civil penalities violations of a scheduling agreement.

Ryan said he would be "very flexible" on the five-minute suggestion.

Melvin Olsen, vice president for traffic at American Airlines, told Ryan, "The big concern I have is that the six airports are not only competitive within themselves. If we reschedule our operations at O'Hare, we are losing our position with those who hub somewhere else."

Airline officials think they can solve the problems at Atlanta, Denver and Chicago, where there is more flexibility to slide flights to adjacent hours. New York is another matter, because almost every minute is already scheduled and there is little room at the airports or in the schedules to slide flights.