The Reagan administration, questioning how much of a role the federal government should play in fish procreation, has proposed closing or giving away nearly half of the Interior Department's 88 hatcheries, which produce millions of fish each year for the nation's inland waters.

In the process, they have hooked a whale of a lot of trouble.

The nation's anglers are furious at what they see as the government's abdication of its responsibilities and the prospect of fewer fish all around, particularly in southeastern lakes and farm ponds.

"A fisherman in Tennessee pays federal taxes and has the right to get something for his money . . . other than defense," said Norville Prosser of the Sport Fishing Institute.

Last year Interior was rebuffed by Congress on 17 of the 31 fish hatcheries it proposed closing. But Congress turned around and cut the funds for six hatcheries Interior hadn't targeted. Now Interior finds itself in court, defending the government's right to close one of those six.

With an annual budget of $25 million, hatcheries may be small fry in the federal pond. But they have long been an outlet for federal dollars in rural areas and a boon to the economy of the areas in whose streams and lakes the fish are stocked.

The first federal fish hatcheries in Neosho, Mo., and Leadville, Colo., were tacked onto appropriations legislation in the late 1880s. The New Deal years later provided a burst of hatchery construction.

The program, however, has long been the target of budget-cutters in Democratic and Republican administrations who ask why the federal government should provide sport fishermen's catch.

But while older, inefficient hatcheries have been closed over the past 50 years, no administration has tried to get rid of so many at once, according to Interior officials and private fishery experts.

The fact that state hatchery facilities outnumber their federal brethren by at least 2 to 1 does little to dampen the fishermen's rage. The 20 hatcheries that Interior has proposed closing or transferring to the states in fiscal 1984 spawn more than 50 million fish annually--trout, salmon, catfish, pike, bass, crappies and the like. A few million of these will grow to catchable size and provide dinner or fish stories for the country's estimated 60 million fishermen.

A crazy-quilt collection of legislation created the hatcheries, and so closing them is not as simple as writing zeroes on a budget proposal. For one thing, some targeted hatcheries--like the Jones Hole facility in Utah--were authorized to compensate for the effect of federal dams or water diversions on natural fisheries.

Many salmon hatcheries in the Northwest were designed to make up for dam construction that kept salmon from going upriver to spawn; some in the Rocky Mountains were designed to mitigate damage caused by federally authorized diversions of Colorado River water.

Other hatcheries have been built in recent years to revive the fish populations of the Great Lakes or to rejuvenate the Atlantic salmon industry. Still others provide fish for waters on Indian reservations, military bases and the government's vast western holdings.

But many hatcheries are also used to stock state-managed lakes, reservoirs or ponds, uses that Interior has decided are a low priority. These are concentrated in the South and Southeast: 19 of 35 hatcheries now being transferred or proposed for transfer or termination are in southern states, including three in Virginia.

Interior is in the process of tranferring two southwestern Virginia facilities, at Wytheville and Paint Bank, to the state. The transfer of the third, Harrison Lake, was blocked by Congress last year.

This year Interior is trying again, arguing that the estimated $2.8 million cost of repairing the dam that supports the hatchery is prohibitive. Supporters of the hatchery, however, contend that repair costs have been inflated to make a better case for giving the facility away.

"The federal government is phasing out raising and providing fish for state management needs or purposes. This is clearly a state responsibility," the Interior Department said in an employe newsletter.

"Fishing is something a lot of people have grown up thinking of as a birthright," counters Pamela McClelland of Trout Unlimited.

"Hatcheries do provide important recreational potential for people . . . . States don't usually have enough personnel and money" to support them, she added. "Our main concern is that there hasn't been congressional overview or citizen input in this process. By budgetary development, the administration is making policy changes."

McClelland's organization is pushing for an oversight hearing, hoping that some congressman whose constituents are losing their fish will take an interest.

New Mexico and Colorado aren't waiting around for Congress, however. They have sued Interior to block the transfer of the Jones Hole hatchery, which stocks reservoirs in those states with sport fish.

"We may be a little selfish," said Richard McCleskey, chief of the New Mexico fisheries division, "but we're worried about New Mexico. When you start looking at this from an economic standpoint, it's a significant impact."