D.C. budget officials told congressional aides yesterday that private auditors have determined that the city completed fiscal 1981 with a $68 million surplus, according to knowledgeable sources.

The $68 million figure, to be officially announced next week, is nearly 10 times greater than the $7 million surplus forecast by Mayor Marion Barry last July and a far cry from the $60 million deficit that city officials were fretting about 11 months ago.

Barry cited the potential deficit to justify major cutbacks in city programs and the elimination of hundreds of city jobs, and to enlist congressional support for a maximum federal payment for the city and the authority to sell bonds to refinance nearly half of an accumulated debt then estimated at $388 million. The city got the federal payment, but not the bonding authority.

Several members of the City Council, who in recent months have sharply criticized Barry for playing tricks with the budget and revenue estimates, reacted with anger or suspicion yesterday to reports of a $68 million surplus.

"I am being jerked around and I don't like it," said council member John A. Wilson (D-Ward 2), chairman of the Finance and Revenue Committee. "I went to the wall on Barry's last budget and we did not have to do it."

Council member John L. Ray (D-At-large), an announced candidate for mayor, said that, if true, the $68 million surplus indicates incompetence among the mayor's budget experts.

"You're paying those professionals $40,000 to $50,000 a year and they can't even count," Ray said.

City administrator Elijah B. Rogers, Budget Director Gladys W. Mack and several of the mayor's other top financial aides spent an hour yesterday briefing the congressional staff members on the audit for the fiscal year that ended Sept. 30, 1981, prepared by Arthur Andersen & Co. But they later refused to discuss the content of the briefing with reporters.

One source who attended the meeting said, however, that city officials told their Capitol Hill audience that the city's tax revenue estimates last July were far too conservative.

The officials said the total tax yield was $1.0789 billion or about $49.4 million more than previously estimated, according to one source, in part because some taxes had been paid earlier than expected.

"They haven't been the most accurate in revenue projections," one source said of the city's finance officials. "It appears that either they've had an extremely good year or they were way off in their estimates."

Congressional aides also were told that the city government underspent the amount of money in the 1981 budget by about $7.7 million, as compared to $22.3 million in overspending the previous year, when there had been a budget deficit of $105 million.

The source suggested that D.C. officials may have intentionally underestimated projected revenue to exaggerate the city's economic plight when it was lobbying Congress and the White House for the annual federal payment to the city. Late last year, Congress approved a record high $336.6 million federal payment for the current fiscal year.

Two persons who attended the meeting said city officials gave an oral presentation and did not distribute any copies of the audit.

Sources said the city officials cited a checkbook surplus of about $58.4 million in operating expenses in the general fund, which translated into the equivalent of a $68.3 million surplus when the figures were adjusted to conform with generally accepted accounting practices.

Those figures were in sharp contrast to the 1980 fiscal year, when the city had a checkbook deficit of about $53.1 million, which nearly doubled when adjusted.

Aides also were told at yesterday's briefing that the city's accumulated debt was now $377 million--not $388 million as previously estimated. The surplus will be used, Rogers told reporters yesterday, to reduce the accumulated debt.