American Airlines, which traded away 10 of its valuable airport landing rights at National Airport for landing slots at other choice airports, now wants other airlines to agree to give it 10 new slots at National.

The ensuing flap has resulted in the failure of the airlines to agree on how to allocate the 35 additional slots that the Federal Aviation Administration is making available to the airlines at National this fall.

Also contributing to the impasse is Altair Airlines, which this summer sold its 10 slots at National -- five roundtrip flights a day -- to People Express Airlines for almost $1.8 million. Last week an Altair representative said his airline wants 16 of the 35 available slots -- the same number it had last July.

The additional number of flights being made available at National is the result of FAA's removing National from a list of 22 airports whose operations have been restricted since the striking air traffic controllers were fired last August.

Now the number of flights allowed at National will be controlled by the government's metropolitan airports policy, which allows a total of 555 daily commercial flights rather than the 520 that has been the upper limit for the past year.

American, Altair and many other carriers suffered flight cutbacks at National as a result of the air traffic control restrictions. But most airlines held on to whatever National slots they had and sought to increase them when the FAA allowed the airlines to sell and swap slots there.

Faced with distributing 35 extra flights, officials of most of the airlines were irked by the requests from American and Altair for more slots just after they had given some up. "It's blackmail," said one official. "Airlines that voluntarily withdrew flights from National shouldn't be able to come back in here and get more flights."

Some officials argued the two airlines could swap or sell them again.

Having failed during the last two weeks to reach an agreement on how to distribute the newly available slots, the airlines' representatives scheduled another meeting for Sept. 11.

Some officials said they are worried that if the impasse isn't broken, the government may decide not to distribute the 35 extra flights or may auction off the new slots.