Passengers flying into Washington National Airport yesterday were delayed by as much as 30 minutes because of an air traffic control slowdown, airline and Federal Aviation Administration officials said.

The slowdown comes three weeks after Professional Air Traffic Controller Organization (PATCO) warned that such actions were possible if airlines did not permit controllers to make free, unconditional "familiarization" flights to Europe and the Far East.

A PATCO spokesman officially denied that a slowdown was under way. But Harry Hubbard, chief of the air traffic control tower at Washington National, said, "We have one. We're getting about 10 fewer operations per hour than we normally would in weather like this." Flying weather was superb through most of the East yesterday.

American Airlines diverted four flights from National to other airports yesterday after the flights were held in circling patterns over the National approach routes.

"We ran to our limits on fuel reserves and simply had to go to alternate airports to get down," American spokewman Larry Strain said. The controllers, Strain said, "are mad at the Air Transport Association (the airlines' lobby and they're trying to screw everybody."

Allegheny, Eastern, Trans World and United airlines all reported landing delays at National of from 10 to 30 minutes. But not all were willing to blame the controllers officially.

Airline officials are concerned that the controllers are begining selective slowdown that would affect one or two airports a day rather than the entire nationwide system. Washington National is a good place to start because of its high visibility with congressmen and other influential people.

PATCO president John Leyden said in a press conference May 23 that several airlines have angered the controllers by refusing to let them ride free in cockpits as observers of overseas in-flight techniques.

Such "familirization" flights for controllers have long been standard on domestics routes. But airline officials have grumbled privately about what they claim is the controllers' proclivity for choosing January flights to Miami to gain their cockpit familiarization. The opportunity for international flights was added in the controllers' most recent contract with their employer, the FAA.STSince then, "we've had requests from a controller in Charlottesville to take a flight to Auckland, New Zealand from one in Miami to go to Tokyo via Honolulu and from one in Alton,III., to go to Tokyo. There are a lot of others I can give you," an Air Transport Association spokesman said.STSpokesmen for both TWA and Pan Am, the leading international airlines, said yesterday that they have no objection to familirization flights in principle, but that they cannot always guarantee a cockpit seat on a given flight, which they say the controllers want.

"We get 400 requests a month from controllers, and we accommodate nine out of 10 of them," a TWA official said.

The Air Transport Association obtained a court order last week required rt Association obtained a court order last week requiring the controllers to abide by their contract with the FAA. Another hearing in that case is scheduled in federal District Court in Brooklyn on Friday.