The leaky and financially shaky Kennedy Center here is threatened with a mounting, multimillion-dollar debt that will require either a government bailout or cuts in artistic and cultural performances, the General Accounting Office warned yesterday.

A report issued yesterday by GAO, Congress' auditing arm, spotlighted a long-simmering but still unresolved issue. By December of next year, the Kennedy Center will owe the U.S. Treasury about $35.4 million, but the center has not set aside funds to meet its debt.

"It never had any. It was just breaking even," Roger L. Stevens, the Kennedy Center's chairman, said in a telephone interview last night.

The new study of the center's financial predicament was made public only two weeks after the Kennedy Center began solving one of its other problems - leaks.

The center announced early this month that all three of its restuarants will be closed for as long 12 weeks this winter and that its concert hall will be shut down for about five weeks next summer to allow repairs of extensive damage caused by water leaking through the stately memorial structure, which overlooks the Potomac River.

The long-awaited repairs required a $4.7 million appropriation from Congress, the same forum in which the center's financial troubles appear likely to be scrutinized. "The Kennedy Center cannot meet all of its financial obligations to the federal, government and continue to conduct the full range of performing arts and public service activities which it was created to present," GAO said in its new report.

"Only Congress," the auditing agency added, "can make both the value judgments and the trade-offs required to resolve this situation."

In prospect, apparently, is a financial deal among officials of Congress, the Kennedy Center, the Treasury Department and the Interior Department, which helps maintain the building. An earlier deal was struck on a related financial problem between the Kennedy Center and the General Services Administration, the federal agency that oversaw the center's construction.

The Kennedy Center's chief financial dilemma stems from a $20.4 million loan, made in the form of revenue bonds, from the U.S. Treasury to finance construction of the center's 1,400-car garage.

Interest due on these bonds will bring the center's total Treasury debt to about $35.4 million by Dec. 31, 1978, when interest payments currently are scheduled to begin. Interest due on the bonds, GAO noted, will accumulate at more than $2 million a year from that time.

Stevens offered two explanations last night for the center's incapacity to make these steep interest payments. First, he said, interest rates were far higher when the bonds were issued than when they were initially proposed, creating a debt outstripping the center's modest income. Second, he noted, the bond issue initally had been set at about $15 million but later was increased because of construction cost increases due to inflation.

The GAO study also pointed out two other financial issues.

The Kennedy Center, GAO said, still owes the General Services Administration several hundred thousand dollars for unpaid construction expenses - including $321,000 in unpaid telephone charges as of Sept. 30, 1976.

In a letter to GAO, Stevens took issue with this statement, arguing that the center's debts to GSA had been resolved in a 1976 agreement calling for gradual reimbursement over a period of years. "Accordingly, the implication that the Kennedy Center's obligation is overdue is not correct," Stevens said in the letter.

GAO also concluded that the Kennedy Center is paying too small a share of the center's maintenance costs. Under a formula worked out in 1971, the center pays 23.8 per cent of the maintenance expenses, and the National Park Service pays the remaining 76.2 per cent on the theory that the center is a national memorial.

In his letter to GAO, Stevens disputed this contention, saying the center already is "paying more than its appropriate share" and urging that the National Park Service, an Interior Department agency, pay the building's entire maintenance costs as part of a possible deal that, he said, would resolve the center's over-all financial problems.

The Interior and Treasury departments appear to view the GAO findings from different points, with Treasury expressing a more conciliatory outlook.

Interior, in a letter to GAO, agreed that a new cost-sharing formula should be negotiated - apparently to find one that would decrease National Park Service expenses and increase those of the Kennedy Center.

But Treasury, in a separate letter, expressed reluctance to put a financial squeeze on the center, saying, "It would be incongruous for the Treasury to press its claim to the limit."

"As with any lender, the department occasionally has to accommodate a bad loan situation and refrain from extracting every possible penny from a financially impaired borrower or imposing conditions that may aggravate the situation," the Treasury letter said.

Stevens, suggesting that the Kennedy Center and the federal government reach a new deal, proposed two possibilities.

If the Treasury will forego interest on its bonds and Interior will pay the entire maintenance costs, Stevens suggested, the center will agree to repay the $20.4 principal on its Treasury debt in annual installments of $1 million.

Or, if Treasury will forego the interest payments but Interior insists on paying only part of the center's maintenance costs, Stevens said, the center will agree to repay the $20.4 million principal in $500,000 installments.

But if neither deal is struck and the government insists on collecting its debts in full Stevens warned in his letter to GAO, "the unavoidable consequence would be to reduce the scope and quality of [the Kennedy Center's] public service programming, including the free events and children's and theater productions which it now regularly mounts."