The National Transportation Safety Board reported yesterday that the nation's air traffic control system is suffering from several significant safety problems despite the excellent record it has compiled since President Reagan fired 11,400 striking controllers in August, 1981.

In a letter to the Federal Aviation Administration, which operates the system, the board said that, "Based strictly on the absence since the strike of a significant number of accidents attributed to air traffic control factors, the ATC system has been operated safely."

However, it said, problems in the system "indicate that the margin of safety is less than the safety board believes to be desirable."

Nine recommendations to the FAA were backed up by an 84-page report detailing months of interviews, surveys of controllers and other checks by board investigators.

The board said it is concerned about four things:

* "Incomplete reporting" of errors by controllers and pilots that result in planes getting too close to each other. The FAA, the board said, concentrates on disciplining controllers who err, which means that controllers tend not to report their errors and the FAA tends not to get at the roots of their causes.

* The FAA has not found a way to monitor and correct excessive workload, fatigue and stress among controllers, most of whom have had few vacations and have worked many hours of overtime to keep the air traffic system functioning since the controller strike 22 months ago. As restrictions on the number of flights are relaxed and traffic increases, "the controllers' workload is increased and the margins for error are reduced logarithmically."

* Front-line air traffic control supervisors, who kept the system running after the strike by pulling chairs up to the radar screens, are continuing to handle traffic almost as often as they supervise. When they do, no one supervises, although "the need for direct supervision still exists and must be provided."

* The FAA's Flight Service Stations, which provide weather information and other aid to nonscheduled aviation users from pleasure pilots to small airlines, have been unable to meet demand. The result is that many unscheduled airline and small plane pilots have chosen to fly with outdated weather information and without benefit of air traffic control services they should have used.

To deal with the problems, the board recommended, among other things, that the FAA:

* Postpone planned increases in air traffic volume until sufficient controllers are trained and qualified and supervisors can return to supervising.

* Develop measures of determining and alleviating stress among controllers.

* Reprogram FAA's air traffic computers so they will detect and report controller errors that can be analyzed.

* Permit controllers to report mistakes and errors by themselves and others without fear of disciplinary action.

* Assign adequate staff and equipment to Flight Service Stations so the aviation community will get better weather and flight plan information.

The safety board has no authority to require regulation or change, it can only nag. The FAA is required to acknowledge board recommendations, but is not required to adopt them.

FAA spokesman Dennis Feldman said the report would be studied. "We're pleased that the board did not find the system unsafe," he said. "Our feeling is that the best empirical evidence of any safety matter is the record itself." No accidents have been attributed to strike-related causes, the board said.

The report is the second major study the safety board has conducted since the strike, and both have concluded that flying is still basically safe.

There was substantial debate among the board's five members as to how harsh this new report should be in raising problems. The issue was resolved when members Donald D. Engen and Francis H. McAdams filed a concurring comment that said, "In our view, the tone of the report implies a lack of safety that is not supported by objective data of the day-to-day operation of the system."

Board members not bothered by the tone of the report and voting for it were Patricia A. Goldman, G.H. Patrick Bursley and Chairman Jim Burnett.

The report comes at a time when Transportation Secretary Elizabeth Hanford Dole and FAA Administrator J. Lynn Helms have been telling Congress that the air traffic control system is now capable of handling as many flights a day as it did before the controllers struck.