Air travel remained safe after air traffic controllers went on strike Aug. 3, but safety could be compromised if heavy workloads wear down the reduced staffs running the control centers, a lengthy study by the National Transportation Safety Board has concluded.

Board Chairman James B. King said yesterday that board investigators found no evidence that the Federal Aviation Administration had put unqualified people to work in the control rooms, as the Professional Air Traffic Controllers Organization (PATCO) has charged.

The FAA was able to maintain safety standards, King said, by cutting flights to levels the smaller work force could handle, about 75 percent of pre-strike levels, and by smoothing traffic peaks. Though the study looked only at the first two months after the Aug. 3 walkout, board officials said they knew of no safety problems after that period.

But board members questioned FAA statements that new controllers can be trained fast enough to return air traffic to its former levels by mid-1984. King called that projection "extremely optimistic."

The board also strongly criticized the FAA's handing of employe relations. Unless they improve, King said, "we'll be faced with another labor dispute downstream." Staff members said that many of the causes of the poor relations had not been corrected.

About 11,500 of the FAA's 17,000 controllers were fired for taking part in the strike, which federal courts ruled to be illegal. At present, about 10,000 non-striking controllers, supervisors and military controllers are staffing the control towers and regional "enroute" centers.

The board, an independent federal agency, ordered its study in the wake of charges that the interim system was unsafe. Between Sept. 1 and Oct. 9 its investigators visited 45 airport towers and control centers and interviewed about 220 working controllers and supervisors, as well as strikers and aviation industry officials.

FAA and PATCO officials declined comment on the board's report until they had had time to study it in detail.

Yesterday, the board underscored recommendations it made in October that the FAA monitor stress and fatigue closely among working controllers. "The work keeps coming at you in a steady pace," King said. "It's almost a production line." But King said he knew of no case after the strike in which stress had contributed to a safety violation.

The report the board approved yesterday said that "the FAA has no formal program to monitor stress and fatigue, nor does it consider stress a major problem."

The board made three new recommendations yesterday, calling on the FAA to encourage controllers to report safety errors to the National Aeronautics and Space Administration, to take extra care in matching new controllers and jobs in field offices and to standardize traffic control training and procedures.

Yesterday's session between the board and staff members included lengthy discussion of allegations that before the strike PATCO members held excessive power in the facilities, intentionally overloaded computers and created a stressful working environment.

Staff members gave contradictory responses to questions over whether poor labor-management relations and alleged overstaffing had affected safety, and they acknowledged that many of the charges against PATCO had not been checked with the union.

Other conclusions in the board's report:

* FAA statistics on reports of violations of aircraft "separation" rules dropped from reports of 1.83 incidents per day in August and September, 1980, to .77 per day in the same period in 1981.

* Computer "down time" decreased in almost every air traffic control facility after the strike.

* Every investigated allegation of medically unfit or unqualified people working as controllers turned out to be unfounded. Between 75 and 100 such cases were looked into, according to a board spokesman.

* Some supervisors and staff members recertified to work as controllers were reported not fully proficient in the job for two weeks.

* Floor supervisors got poor support from middle and upper-level management in dealing with controllers before the strike. Management changes must be made if problems which existed before the strike are to be resolved. The board did not specify what changes should be made.

Because the study dealt only with the first two months of the post-strike air control system, the board plans to do another study, a board spokesman said.