The National Park Service has ordered the closing of one of Washington's three public golf courses, threatened to close a second and is considering cutting back the size of the third.

Citing apparent financial losses and the cancellation of insurance coverage by a private concessionaire, the park service said the Langston golf course on Benning Road NE by the Anacostia River was closed down last week for an indefinite period.

Also, Rock Creek golf course near 16th Street above Military Road NW may be closed if a new private operator cannot be found, the park service said, and 18 of the 36 holes at East Potomac Park golf course near Hains Point SW may be turned into a picnic area and playing fields.

The three are the only major public golf courses in the nation owned by the federal government, other than those on military bases. The park service also has two small nine-hole courses at Yosemite National Park and Cape Cod National Seashore.

The Langston closing came during an apparent contract dispute with golf pro Lee Elder, whose family firm has operated the 18-hole course for the park service since 1978. It is the second closing in 10 years for Langston, which has been lightly used and lost money most of its 47 years.

The new order to close Langston came after Elder notified the park service he had canceled the required insurance policies for the public golf course.

Rose Elder, who manages Lee Elder Enterprises Inc., said the firm canceled the $10,000 policy "because of the unresponsiveness" of the park service in negotiating changes to their concession contract. Park service officials said there has been a dispute over specific terms of the contract, which expires in 1983 and under which the Elders promised to undertake a $160,000 improvement program at Langston. Rose Elder said they have made "in excess of $260,000 of improvements" to the course and the clubhouse under terms of the contract.

Park service spokeswoman Sandra Alley said the Elders gave the government no reason for the insurance cancellation. Federal concession regulations require insurance to protect government properties and the public using them.

The closing of Langston, built originally for black city residents in 1934 during the Roosevelt administration, came amid widespread reports that the golf course was again losing money, was in poor condition and was suffering a sharp drop in patronage.

Alley said only 21,500 golfers played at Langston in 1980, 8,000 fewer than in 1979. Langston reportedly has been doing even worse this year, although Rose Elder contended the park service figures are wrong and more golfers have been playing at Langston every year since 1978. She said she didn't have exact figures immediately available.

As for the other two golf courses, the park service says it will advertise for a new Rock Creek operator within the next few weeks to replace the present operator, who is quitting, and soon will hold public hearings on reducing East Potomac from 36 to 18 holes.

The park service says it will close Rock Creek if it cannot find a new operator. It says it is considering converting 18 holes at East Potomac into picnic grounds and playing fields because the adjacent park area often becomes overcrowded and needs expansion.

Ironically, patronage at Rock Creek and East Potomac has increased in recent years, though not enough, at least in the case of Rock Creek, to make a profit, say the operators. In 1980, according to Alley, 41,500 golfers played at Rock Creek (up 9,500 from 1979) and 79,200 at East Potomac (up 11,100 from 1979). Both reportedly are doing even better this year.

Severine Leoffler Jr., whose family operates Rock Creek and East Potomac, says the problem is that the area is saturated with golf courses. There are "something like 70 golf courses in the Washington area," too many to survive, he says. "Even in 1968, I told the park service there was no future for Langston . . . and that Rock Creek ought to be phased out, too."

The Leofflers haven't been the only ones saying the city's golf courses are endangered financially. A 1979 consultant's study for the park service concluded the three public courses "have all been allowed to deteriorate over the past 10-15 years" and "constitute a real investment risk" to any operator unless the federal government is willing to make at least $2.1 million in improvements to the courses. The study said at least 41,000 golfers must play each of the 18-hole courses a year to make money for an operator.

The park service has not asked Congress for the money recently to improve the courses, or for $1.2 million needed to open a new Oxon Cove Golf Course, partially completed on top of a sanitary landfill near the Blue Plains Sewage Treatment Plant in the District.

Despite severe budget cuts and the loss of 300 employes, says regional director Manus J. Fish, the service has managed to put $300,000 into Langston and $200,000 into Rock Creek and East Potomac golf courses in the last three years.

"We lost money for 37 straight years at Langston before we gave it up in 1973," says Leoffler, " . . . and we've lost money for the past six years at Rock Creek," which is why his family has now asked the park service to find another operator or close it. In the past, the profits from the huge East Potomac course covered the losses at the other places, Leoffler said.

The federal government has opened and closed several courses here over the years, including one along the Anacostia River, removed when I-295 was built, and a course at Fort Dupont Park, closed in 1971 for lack of use and because golfers were often robbed. In the 1920s, the Leofflers built two small public courses near the Lincoln Memorial, one for whites and one for blacks.

The prices at Leoffler's golf courses have always been among the lowest in the nation, says Leoffler. The Rock Creek and East Potomac prices are still about half that of other public golf courses around Washington: $3.75 for 18 holes on weekdays and $4.50 on weekends. The prices at Langston have been somewhat higher: $5 for 18 holes on weekdays and $6 on weekends.