The D.C. City Council yesterday tentatively approved a $1.89 billion city operating budget for next year that includes $20.7 million more for the public schools than had been proposed by Mayor Marion Barry.

To achieve the extra spending, the council voted to shift funds that had been earmarked by Barry for retiring a portion of the city's accumulated deficit and for other programs--chiefly one designed to improve the city's financial management system.

Gladys W. Mack, the city's budget director, said yesterday that Barry would support the increased spending for schools provided the overall budget is balanced on the basis of the mayor's current revenue estimates and requests for additional taxing authority.

"We would not quarrel with the recommendation for education," Mack said. "The mayor certainly has expressed his commitment to quality eductation. Our only concern is that the council takes proper action to balance the budget."

The council, which met yesterday as a committee of the whole, is scheduled to take final action on the budget tomorrow.

The total operating budget exceeds Barry's overall recommendations by only $9,000 and the capital improvements budget of $88.5 million was nearly identical to that proposed by Barry, with the exception of $240,000 added for reconstruction of a stretch of Blair Road NW.

The council yesterday tentatively restored funding for two fire stations on the edge of downtown that the mayor proposed to close, and it established a $1.13 million contingency fund to help offset anticipated cuts in federal spending for social welfare programs.

But the most significant change made in Barry's spending plan was to increase the school system budget--a popular move in a year when the mayor, the council chairman and six other council seats are up for election--while placing the issue of the city's accumulated debt squarely on the back burner.

Council members John Ray (D-At-Large) and John A. Wilson (D-Ward 2), both announced candidates for mayor in the Democratic primary, opposed deferring action on retirement of the city's long-term debt.

Barry had proposed to spend $285.78 million in fiscal 1983 on the public schools, including funds for anticipated teacher salary increases. This was about $26 million less than had been sought by the D.C. school board and recommended by the council's Committee on Education.

Yesterday, the Committee of the Whole voted to shift to the schools an additional $16.5 million that Barry earmarked for debt retirement and $4.2 million in funds from other departments and programs.

Many of the council members indicated that they saw no need to set aside $16.5 million for debt retirement next year after a recent audit revealed that the city ended the past year with a $68 million surplus.

The unexpected surplus, combined with changes made in the city's accounting procedures, resulted in a reduction in the deficit from $388 million last year to $309 million at present.

Council members who have said that they suspect that the mayor's revenue estimates for the coming year again may prove to be too conservative said they were confident in spending more for education, while reducing the commitment to the deficit.

"Last year we paid out $68 million toward retiring the deficit , so we're way ahead of the game, in one sense," said council member Betty Ann Kane (D-At-Large), another announced candidate for mayor.

Council Chairman Arrington Dixon insisted that the council's action did not reflect a lessening of concern about the city's long-term financial problems, but merely a "focusing of efforts on one area that we care about--education."

Wilson, however, said that the action would be detrimental to the city's efforts to gain access to the private bond market and would end its reliance on the U.S. Treasury for long-term borrowing for capital improvements.

"We now effectively have no reasonable program to retire the debt, except to hope the mayor underestimated the revenues," said Wilson, chairman of the Finance and Revenue Committee.

Wilson and Ray briefly pushed for an alternative plan to increase funds for the schools by imposing an across-the-board reduction in spending for other departments of three-tenths of 1 percent. Wilson withdrew the proposal before it came to a vote.

The council tentatively agreed to another Wilson proposal to budget a token $2.7 million for debt retirement next year, with funds taken from the Department of Environmental Services.