Representatives of 24 airlines operating out of Washington's National Airport hammered out an agreement yesterday distributing the airport's limited landing and takeoff privileges among them for the summer season.

Agreement came largely because the airlines agreed to hold down summer takeoffs and landings -- called slots -- to the number they plan to operate on April 1. Most of the airlines had wanted to boost significantly the number of their flights during the peak summer travel season.

An important contribution to reaching an agreement was made by New York Air, which agreed to hold its request for slots to the 18 a day it now has, even though it plans to operate at least 36 flights.

New York Air already has 28 operations a day at National -- 10 more than its present slot allocation -- and it will be landing and taking off 36 times a day beginning Sunday, when it starts nonstop service between Washington and Boston.

New York Air representatives made it clear that agreement to the slot allocations is contingent on the airline's ability to continue operating the additional flights "subject to air traffic control conditions," as it currently is doing.

The airline, which began Washington-New York service in December, has been flying the extra flights legally under a provision in the Federal Aviation Administration's "high density" airport rule that applies to National Airport. The provision -- also used by commuters and private planes -- essentially allows extra flights to land without slot "reservations" as long as there is good weather and so-called visual flight rules prevail.

In bad weather, when instrument flight rules may be imposed, flights may be limited to those with the slots.

The airlines' agreement on National operations gives the new leadership of the Department of Transportation time to review the National Airport policy -- which limits commercial airlines to 640 slots a day -- without the pressure of immediately having to step in and distribute the slots. DOT was faced with that task last fall when the airlines could not agree among themselves on an operating formula for the winter season, which runs from the end of daylight savings time in October to the beginning of daylight savings time in April.

The agreement, which took repeated meetings to reach, would have been almost impossible had the airlines had to cut the number of permitted flights a day from 640 to 522 under a DOT policy that was scheduled to take effect April 26. DOT Secretary Drew Lewis formally proposed a six-month delay in the policy to give the new administration time to review it thoroughly.

In other developments yesterday:

Delta Airlines this week dropped its Washington-Boston $108 fare to match the $69 fare that New York Air plans to charge for its new nonstop service.

A federal appeals court in New York City rejected the attempt by the Airline Pilots Association to bar New York Air from operating on grounds that the new carrier, which so far has no unions, provided inferior wages and working conditions and was indifferent to safety regulations.

New York Air appears to have decided to fly between New York and Cleveland next. Although its officials declined to comment, an ad in a Cleveland paper said New York Air was seeking employes in Cleveland.

The U.S. Court of Appeals in San Francisco refused to grant Continental Airlines an injunction to halt a $13-a-share tender offer for almost half the airline's stock by Texas International Airlines.