The Reagan administration's budget-cutting sharks have claimed their latest victim. They swallowed the entire 108-year-old National Aquarium so quickly that the aquarium's staff never even saw the circling dorsal fins.

The amount consumed -- $280,000 -- is a mere minnow when compared with the saving the administration hopes to achieve at other federal agencies.

But for the National Aquarium, founded in 1873 under President Ulysses S. Grant, it amounted to every penny of its fiscal 1982 operating budget. So, come Oct. 1, director Craig Phillips says the aquarium will close its doors once and for all.

Its several hundred living exhibits, including a snout-nosed gar that has been an aquarium fixture for 17 years, will either be given to other aquariums or, if they're of local origin, dropped into the nearest stream.

"They are paring the national federal budget to the bone," mourned Phillips, who said he first learned of the cut Tuesday. "And we are one of the bones, apparently."

The National Aquarium is not, to put it bluntly, one of the capital's tourist hotspots. Small and underfunded for much of its existence, it has been visited by fewer than 500,000 people a year, well below the attendance figures of such competitors as the Air and Space Museum (7.2 million), the National Zoo (3.5 million) and even the Botanical Gardens (1.9 million).

But it is free, it is in the heart of downtown Washington (in the Commerce Building at 14th and E Streets NW) and the 250 species of marine life on display are intimately close and alive.

"It's worth it," said Mark Dempsey, a pet store employe who had dragged his unwilling friend, Debby Worton, to see it yesterday. By the time she left, she was a covert, too.

"It's nice. These things are alive. It's not like the murals at the Museum of National History," she said.

The National Aquarium is generally filled with children on school expeditions, inner-city residents and an occasional tourist. If it were allowed to charge an entrance fee, it could survive. Phillips said. But federal law prohibits it from doing so. And it cannot cash donations, either.

Senior officials with the Fish and Wildlife Service, the National Aquarium's parent organization, not the White House, were the ones responsible for the decision to cut the entire aquarium budget. They did so, they said, because they have other more pressing responsiblities, such as helping to preserve migatory birds, and the Office of Management and Budget had forced Fish and Wildlife to cut something.

"We've had $65 million cut from the Fish and Wildlife Service budget alone," said Alan Levitt, a service spokesman. "Overall, the Interior Department will have to cut about $1 billion."

Bill Daugherty, chief of Fish and Wildlife's Hatcheries and Fishing Resources Management division, said the service has not considered asking for charge admission or accept outside donations. Phillips said he may seek such authorization, however.

In any event, the future does not look bright for the acquarium. Indeed, the budget sharks have been nosing around the facility ever since the late 1960s. That was when a $10-million authorization to build a National Fisheries Center and Aquarium at Hains Point was shelved.

But as insignificant as it is, the aquarium has had influential friends. The late legendary FBI director, J. Edgar Hoover, used to house his outdoor goldfish inside the aquarium over the winter. And just a few months ago, one of Sen. Strom Thurmond's (R-S.C.) children celebrated a birthday by taking friends to the aquarium after cake and ice cream.

Sen. Thurmond's office said yesterday he sadly recognized the need for some budget cutting, including that of the National Aquarium.

So the Caribbean eel, the piranha, the lobsters and file fish, the trout and the lemon shark will have to find calm waters elsewhere. Some may actually end up at Baltimore's new $21.3-million National Aquarium, built by the city with about $2 million in federal funds, when it opens in July.

But it will cost up to $4.50 to see the fish there.