Eastern Airlines yesterday responded to New York Air's proposed low-fare service between Washington and New York by matching the new competition's lowest fare -- but only during a 24-hour period each weekend.

Eastern announced it would cut oneway fares on its shuttle service from $59 to $29, New York Air's off-peak price, but only on flights between noon Saturday and noon Sunday.

The new $29 fare will take effect Dec. 13 and, in addition to the Washington-New York shuttle, it will apply to Eastern's flights form Washington to Newark and New York's JFK International Airport as well as to its shuttle flights between New York and Boston. The Miami-based carrier now offers a roundtrip weekend excursion fare of $77 on the shuttle.

"This fare is directed toward generating more family and discretionary travel between these cities on weekends, to catch Broadway shows, attend sporting events, shop or for any other personal reasons," Russell Ray, Eastern's senior vice president of marketing, said yesterday. New York Air, whose services are scheduled to begin Dec. 14, the day after the Eastern price-cut, was not mentioned in Eastern's announcement.

New York Air, an affiliate of Texas International Airlines, plans to operate 10 roundtrip weekday flights and eight roundtrips on the weekends with a two-tier peak/off-peak reserved-seat pricing system. Fares on eight of NYA's 10 daily flights will be $49 each way, while a lunchhour and night flights will cost $29 each way.All seats on the weekend flights will cost $29.

Until yesterday, Eastern had been silent on its possible response to its new competitor except for the start of a new advertising campaign which stresses the benefits of the shuttle for consumers. Full-page ads in major newspapers on the East Coast have emphasized that the shuttle offers an unusual hourly no-reservation walk-on air serivce that guarantees a seat to anyone at the gate before the scheduled departure time. "Imagine life without us," one admonishes its readers.

Even before it has started, New York Air has won an important source of business. Yesterday, the General Services Administration announced that New York Air was among nine airlines to win contract awards for flying federal employes on official business on 43 U.S. air routes. NYA offered to fly the employes between Washington and New York for $29 each way. Altogehter, GSA said the awards would save the governement $7 million over the next six months.

Meanwhile, the Civil Aeronautics Board yesterday held oral arguments in its proceeding into New York Air's fitness and set Dec. 11 for its final decision. New York Air is expected to be awarded its certificate despite some vociferous union opposition. During the argument yesterday, lawyers for three unions argued that Texas Air Corp., New York Air's parent company, set up the new affiliate -- instead of using its other affiliate, Texas International Airlines, for the new service -- specifically to avoid the higher wages and work rules in TI's contracts.