The Potomac River, stigmatized in recent years as a running sewer, has been cleaned up so successfully, that it is safe enough to swim in, Paul W. Eastman, director of the river's watchdog agency, said yesterday.

To dramatize that belief, Eastman and other officials of the Interstate Commission on the Potomac River Basin are organizing a Labor Day swim-in at the mouth of Rock Creek.

A seven-year-old District law prohibits all body contact with water in the Potomac under penalty of a $300 fine, but Eastman said flatly: "We can now have water-contact activities in the Potomac River."

Eastman said the area between Thompson's Boathouse, near the mouth of Rock Creek, where the C & O Canal National Historic Park begins, and Fletcher's Boat-house west of Georgetown is an "excellent area" for swimming, except after a heavy storm.Storms can foul the river with debris and raise the level of pollution from upstream runoff.

The swim-in (and water ski-in) will not be held. Eastman said, if there are indications of a high pollution level.

Eastman added that any swimming should be done under supervision and should not take place farther downsteam where water quality is poorer.

A swimmable Potomac was promised by President Lyndon B. Johnson 13 years ago. In an often-quoted remark he made Oct. 2, 1965, after signing clean-water legislation, Johnson said: "We are going to begin right here in Washington with the Potomac River . . . I pledge you that we are going to reopen the Potomac fot swimming by 1975."

"I think we've reached that objective," said Eastman, who added that upgraded sewave treatment and other expensive cleanup actions in recent years have begun to pay dividends.

The swim-in, he said, though it is not being sponsored by his agency, has the support of the agency's commissioners representing the District. The agency is an educational, planning and research body created by the District and the states sharing the Potomac watershed - Maryland, Virginia, West Virginia and Pennsylvania.

Eastman said the incidence of fecal - has been consistently within limits counts of fecal coliform indicate the any confrontation over the 1971 law banning water contact.

Eastman said the incidence of focal coliform - the primary indicator of whether water is safe for body contact - has been consistantly within limists established by the Environmental Protection Agency.

Fecal coliform is the bacteria found in animal and human waste. High counts of fecal foliform indicate the presence of pathogens that can cause gastrointestinal upsets, typhoid and other diseases.

The chief of the District's water-quality office, John Brink, disputed Eastman's contention. "I would recommend against the swim-in," he said. "I would say that right now you can't depend on the quality of the river."

He said coliform counts "fluctuate widely. They may go down as low as 50 per 100 milliliters and then up to as much as 250,000 or even higher." The fluctuations can occur in short periods, especially after heavy rains which wash agricultural manure into streams emptying into the Potomac, Brink said.

Water is considered safe for swimming under EPA guidelines when the coliform count is 200 parts per 100 milliliters.

The most recently tabulated samplings done by Brink's Bureau of Air and Water Quality were taken last year. According to sanitary engineer Narenbra Mathur, water from Fletcher's Boathouse to Chain Bridge failed to meet the coliform standard 33 percent of the time in June, 10 percent of the time during July and 50 percent of the time during the August.

Eastman said official city samplings taken this spring and summer, May through July, were below the maximum in most cases. At Fletcher's Boathouse, for example, he said, the May reading was 200, June's was 2 and July's 17.

Under law, the Potomac could be reopened when five readings within a month are at 200 or below. Eastman said, however, that in no month were more than three samplings taken by city officials.

In answer to Brink, Eastman said: "I agree it's difficult to make urban rivers swimmable. If I were a District official, I would resist, too. To open up the Potomac for body contact would mean more patrolling for safety and monitoring for quality. But I think they (District officials) can work out a system.

"I find it rather ironic that the same people responsible for decisions to spend hundreds of millions of dollars to make the Potomac fishable and swimmable dont' want to make a decision to permit people to benefit from these expenditures."

Eastman said that "if we did a survey, probably 75 percent or more of the people would still think the Potomac is badly polluted. I've heard people say that who should know better."

Improved treatment at the big regional sewage plant at Blue. Plains at the southern tip of the District and the plugging of sewer outfalls along the river have cleaned up the Potomac considerably, Eastman said.

Blue Plains will be upgraded more by July 1980 but some citizen activists say the cleanup is lagging. They argue that pollution from upstream runoff - little of which is treated - more than offsets Blue Plains' improved treatment. They have also contended that the advanced technology now being built into Blue Plains has yet to prove itself at such a massive scale.