The Potomac River, for years so polluted it was called an open sewer, now is clean enough for swimming, Washington's top health and environmental officials have concluded.

A position paper approved by Herbert L. Tucker, director of the city's Department of Environmental Services and scheduled to be sent shortly to Mayor Marion Barry, says the city could establish a safe swimming area along a two-mile stretch of the Potomac between Three Sisters Island, west of Georgetown, and Fletcher's Boat House on Canal Road within the next two years.

"I think you could create a safe bathing beach," said John V. Brink, director of the bureau of air and water quality in Department of Environmental Services and the official who drafted the position paper going to Barry.

He stressed, however, that if a beach and swimming area were established, it would have to be adequately supervised, and swimming could not be allowed during periods of heavy storm flow, which generally increases bacteriological pollution, clouds the water with sediment and produces dangerous currents below Chain Bridge.

The verdict that the Potomac is clean enough for swimming, capping a 14-year, three-quarters-of-a-billin-dollar cleanup effort and a 1965 pledge by President Lyndon B. Johnson, is being greeted with excitement by some area conservationists and officials.

"I think it's terrific," said Paul W. Eastman, director of the Interstate Commission on the Potomac River Basin. "A swimmable Potomac is the most important milestone in the river's cleanup."

"It's a milestone -- absolutely!" said Noman M. Cole Jr., who as director of the Virginia State Water Control Board in the early 1970s was chiefly responsible for forging the local alliance of governments that helped make the cleanup possible.

The impact of the massive cleanup effort, which included overhauling and improving the Blue Plains sewage treatment plant, long the river's biggest polluter, has become more and more apparent recently.

Boaters, driven away by the slimy blue-green algae that once fouled propellers and hulls 10 years ago, are back on the river in ever-increasing numbers. Anglers report that game fish, including the highly prized largemouth bass, are returning, too.

Those are marked changes from the river's condition for most of this century. For years it was a dumping place for raw human and animal waste and industrial effluent. As recently as 1971 the river was so polluted that the city actually made swimming a crime punishable by a $300 fine.

But since 1973 there has been a gradual -- and significant -- improvement in those scientific indicators used to measure the purity of water. Counts of fecal coliform which indicate the presence of human or animal waste (which can harbor microorganisms causing infectious diseases), have dropped steadily as many pipes draining raw sewage into the river have been sealed up. Farther upstream, improvements have been made in sewage treatment plants, while locally officials say the Blue Plains treatment plant has become a much more efficient processor of the area's waste.

As a result, fecal coliform counts now show "that the (river) water is of a high quality for long periods of time," said Brink.

Accordingly, said Tucker, there could be officially sanctioned swimming in the District of Columbia's portion of the Potomac by 1981, two years ahead of the goal set by the federal Clean Water Act. All that remains to be done is to establish a supervised beach for swimming, officials say. Because of budgetary considerations, that may have to wait until next year or the 1981 city budget because the city currently does not have the money it would need to create such a site.

Though Maryland and Virginia have no laws prohibiting swimming in the river, Eastman said, neither has established riverside facilities for bathers.

The city's apparent willingness to consider lifting the ban on swimming in the river was prompted by a Potomac Commission request earlier this summer that the city reevaluate its past refusals to do so.

The commission has been pushing for an end to the ban for some time. Last year, Eastman and other commission officials threatened to hold a "swim-in" at Thompson's Boat House on the river as a dramatic demonstration of their contention that the cleanup had been successful.

Officials in Mayor Walter E. Washington's administration, however, were not enthusiastic about the proposal and the D.C. Harbor Police headed off the demonstration before anyone was able to dive in.

Though the river has improved, many environmentalists are displeased with the continuing progress of the cleanup. They say that they are dubious about the ability of Blue Plains and other sewage treatment plants to clean up pollution in the long run.

In addition, Cole says he is deeply concerned about a new sewer agreement that the District of Columbia, Fairfax County and suburban Maryland have reached with the Environmental Protection Agency on Blue Plains. That agreement would permit local jurisdictions to increase the amount of sewage each pumps to Blue Plains by 5 percent.

Cole said there are not strong enough guarantees in the agreement to ensure that the plant will not become overloaded, as it did in the late '60s and early '70s, and cause another cycle of pollution in the river.

In any event, the Barry administration's new position is likely to brighten prospects for repeal of the 1971 city ordinance banning swimming. Council member Jerry A. Moore Jr. (R-At Large), chairman of the Transportation and Environmental Affairs Committee, plans to hold public hearings on the ordinance this fall.

"The time has come for the council to reconsider the ban," Moore said earlier this summer.

In the meantime, even though Harbor Police "have no opposition to swimming in principle," according to Sgt. Ronald T. Wilkins, swimming is still forbidden. Currents in the river can be treacherous, he said, and until an adequately supervised swimming area is set aside, no one will be allowed to swim.