The District of Columbia is edging toward its long-term credit limit and must tighten management in order to keep building needed public facilities, the U.S. General Accounting Office reported yesterday.

The GAO said that, lacking improved management, the District cannot expect to sell bonds on the private money market-a shift of financial policy that is part of the city's plan for expanding its limited home rule. The city now borrows from the U.S. Treasury to finance capital projects.

The GAO, the audit arm of Congress, maintains a permanent outpost at the District Building. The agency based its report on a study of the District's first aborted effort to finance projects through bond sales.

That effort was blocked temporarily chiefly by Sen. Thomas F. Eagleton (D-Mo.), chairman of the District of Columbia subcommittee of the Senate Governmental Operations Committee. Eagleton sponsored an audit that found the city's books in disarray. He also sponsored creation of a new financial management system that is slated to go into operation later this year.

The GAO study reaches as far back as 1970 and covers the administration of former mayor Walter E. Washington, who was succeeded in January by Marion Barry.

Colin F. S. Walters, assistant city administrator for financial management, said he had not read the GAO report, but was told it contained no surprises. "We realize that management of the capital program is an area that needs our early attention," Walters said.

In its report, the GAO noted that the city's debt-now $1.5 billion for such projects at schools, firehouses, the Metro subway and the downtown convention center-is expected to reach $2.5 billion by 1985.

By then, the debt will be close to the legal limit, which is determined by the level of city revenues-mostly taxes-available to pay off the debt, the GAO said.

The GAO said the D.C. government must set citywide priorities for construction rather than priorities within separate departments. And it said the city must set firm price tags for projects rather than permitting cost overruns that could be met by shifting Treasury loan funds from one project to another. Such shifts will be prohibited under private bond sales, the GAO said.

One such overrun was the Watha Daniel branch library on Rhode Island Avenue NW, which was estimated to cost $772,000 in 1970 but ultimately was budgeted at $1.7 million. The D.C. General Services Department blamed the volatile economy of that period, plus design changes sought by others.

At one point, the GAO posed this question:

"An issue that remains for this (library) and the other projects cited (in the report is-would these projects have been approved had the budget requests accurately forecast the costs and scopes?"