The Reagan administration yesterday maintained its hard line against rehiring fired air traffic controllers, despite growing congressional concern that the Federal Aviation Administration's plans to operate the nation's airways without them may fail.

"There's no way . . . and no reason" to rehire the 11,438 controllers who were fired for walking off their jobs Aug. 3, said presidential counselor Edwin Meese III.

Meese's comments came as two House units issued reports that criticized the administration's handling of the strike and called on it to rehire the fired controllers. A House Post Office and Civil Service Committee staff report questioned the FAA's ability to hire and train an adequate number of replacement controllers in a timely manner. "It appears that by the winter of 1983, the system could be in serious trouble," the report said.

A separate report by the Democratic Study Group, a coalition of House liberals and moderates, said continuation of the nine-week-old strike is costing the government and the public billions of dollars in tax and business losses.

In comments following a speech to the Aero Club, Meese expressed confidence that the administration would win its legal battle to have the striking Professional Air Traffic Controllers Organization permanently barred from representing federal workers. He said it is unlikely that the Federal Labor Relations Authority, which has jurisdiction over federal labor-management disputes, would order both sides back to the bargaining table.

"I can't imagine that happening," because the PATCO strike "is so clearly a violation" of federal law, Meese said. The FLRA is expected to rule on the PATCO case by the end of the week.

FAA officials acknowledge that the air control system has difficulties stemming from the walkout, particularly flight delays in the Northeast and Midwest, but contend they are working to correct them.

Yesterday, they presented updated plans for returning the system to normal within three years. In a presentation to an annual FAA forecasting and planning conference, Raymond J. Van Vuren, director of the FAA's Air Traffic Service, said reduced levels of commercial and private flights would be maintained for about a year and then be allowed to rise significantly.

Scheduled airlines, now operating at about 82 percent of normal flights, are being notified this week of further cuts they must institute on Dec. 1, reducing overall capacity to about 78 percent. Private and business aircraft using the air traffic control system will operate under tighter rules beginning Oct. 19, when the FAA begins requiring them to seek permission for their flights by filing flight plans up to 16 hours before takeoff.

Van Vuren noted that the new reservation system would give the FAA more control over the private flying sector than it has had since the strike began. Representatives of the scheduled airlines had argued that private aircraft were cluttering the understaffed air control system.

"General aviation should be treated equitably, but not equally," said Dan Henkin, a vice president for the Air Transport Association, the scheduled carriers' trade group.

Van Vuren said the FAA expects to have an adequate number of controllers in airport towers by next September. But he said it would take much longer to bring the en-route flight centers -- the control points between airports -- to normal staffing levels. As a result, where possible, the FAA is shifting some functions from those centers to airport towers.

Meanwhile, the government says it is making satisfactory progress in training replacements for dismissed controllers. Mark Weaver, spokesman for the FAA Training Academy in Oklahoma City, said yesterday the school has 920 trainees and would soon have an average daily student enrollment of 1,600 persons. The academy's basic training course runs 17 to 20 weeks. Weaver says that the school will be able to graduate about 5,500 trainees a year.

Van Vuren said the first academy graduates would be arriving at FAA facilities for advanced field training by the end of 1981.

The centers are now staffed by about 9,000 civilian controllers, including supervisors, and 863 military controllers, who will be phased out by Sept. 1982.