The government yesterday stripped the striking Professional Air Traffic Controllers Organization of its right to represent nearly 18,000 Federal Aviation Administration employes who operate domestic airport towers and air traffic centers. But hours later, the U.S. Court of Appeals here temporarily blocked the order by the Federal Labor Relations Authority.

The FLRA decertification ruling came on a 2-to-1 vote by the three-member authority, an independent agency that has jurisdiction over labor-management disputes in the federal sector.

The order was to take effect immediately. If it is upheld by the court, PATCO would no longer have the right to bargain for, collect dues from, represent in grievance procedures, or to act in any other way as an agent for workers it has represented since 1972.

PATCO would become the first federal union permanently barred from representing its constituents. But yesterday's ruling marks the second time the union has been denied representational rights by the federal government. PATCO was decertified for five months in 1971 because of what the government called a strike--and what PATCO called a "sickout"--in 1970.

In its decision yesterday, the authority said PATCO "willfully and intentionally violated" federal law by pulling nearly 13,000 of its members, all federal workers, out on strike Aug. 3. That finding upheld a PATCO decertification recommendation issued Aug. 14 by John Fenton, FLRA administrative law judge. "The record fully supports Fenton's conclusion that PATCO's violation. . . is 'open and flagrant,' " the panel said.

PATCO lawyers argued before the appeals court that the ruling would cause major harm to the union because automatic collection of dues would have stopped today for about 2,000 PATCO members who remain on the job.

Robert Bonner, deputy clerk of the appeals court, said the court issued "a temporary stay until it can get a response from the government," which he said was due Monday.

The FLRA decision was a major victory for the Reagan administration, which had fired 11,438 controllers who had refused the president's back-to-work order on Aug. 5. The administration had insisted that anything less than full decertification of PATCO--ironically, one of the few labor unions to endorse Reagan's presidential bid--would prompt other federal workers to violate antistrike laws.

Transportation Secretary Drew Lewis said the decision--should it be kept in force--clears the way for him to ask Congress for a five-part pay increase package for controllers who remained on the job.

Briefly, the package includes an across-the-board 5 percent pay raise, a 10 percent raise for controllers who act as on-the-job instructors, a 1.6 percent increase--in addition to the general raise--for controllers who continue to upgrade their skills, lunch-period pay that effectively would allow controllers to receive 40-hour pay for 37 1/2 hours of work, and a provision that would allow controllers to receive overtime pay in excess of the $50,112.50 annual cap on salaries for federal civil servants.

Lewis said again yesterday that the administration will not rehire any fired controller.

PATCO President Robert E. Poli said: "I'm as proud of my members today as I was of them on Aug. 3." He said the only mistake he made "was naivete in believing the promises" of candidate Ronald Reagan.