A contentious D.C. City Council yesterday approved a $1.9 billion city operating budget for fiscal 1984, after wrangling for hours over spending levels for the public school system and finally accepting a compromise giving the schools $10 million less than they requested.

In unanimously adopting the new budget, the council rejected several of Mayor Marion Barry's proposals to eliminate or sharply reduce programs. Council members allocated $4.6 million more than Barry asked for General Public Assistance, which aids persons out of work because of disabilities, and voted to continue a public school transportation subsidy the mayor wanted to end.

The council also restored funds that Barry wanted to cut for treating the mentally retarded, paying medical expenses for the poor, job training, helping low-income families buy homes, and operating tuberculosis clinics.

Council members also earmarked $5 million in the budget to help retire the city's long-term debt, an action not requested by the mayor.

In all, the council voted to spend about $5.5 million more than Barry proposed in the fiscal year that begins Oct. 1. But to balance the budget, the council now must approve a package of measures to save money and increase taxes, including:

* A total of $14.4 million in additional taxes and user fees sought by Barry, including a new gross receipts tax on utilities.

* A bill that would raise $3 million more in revenues by bringing the District's income tax form in line with the federal tax form.

* A proposal to shift about $12 million in street lighting costs from the city to the utility bills of D.C. residents--a measure that a spokesman for the Potomac Electric Power Company described yesterday as "ill-conceived, inequitable and possibly illegal."

In balancing the budget, the council also is assuming that the D.C. Lottery Board will raise about $2.5 million more in revenues next year than Barry's budget experts have projected. The mayor warned City Council Chairman David A. Clarke yesterday, before the start of the meeting, that the council would be in violation of the city charter by altering the mayor's revenue forecast.

Clarke, the chief architect of the budget passed by the council, and John A. Wilson (D-Ward 2), chairman of the Finance and Revenue Committee, said that a majority of council members have privately agreed to go along with most of the proposed tax increases.

"We got that agreement before we voted here," Wilson said. "I hope we can hold it all together."

The lengthy five-hour council meeting on the budget was dominated by prickly and occasionally bitter debate over the new spending level for public schools.

Clarke, who worked behind the scenes last week to arrange a compromise agreement with Barry and other council members, repeatedly clashed with Hilda Mason (Statehood-At-Large), chairman of the Education Committee and a staunch ally of the school board.

Mason insisted that the school board needed $2 million to $4 million more than the council finally approved and complained that the council wasn't treating the school board with the proper respect.

"If they're nitwits, then we are too, because we were elected by the same people," Mason snapped during a particularly tense point in the debate.

The D.C. Board of Education, with a current budget of $306 million, requested $336 million for the coming year. The mayor originally recommended that the Council grant the schools $318.5 million, but over the weekend agreed to Clarke's proposal for $326 million.

School board officials said they had little choice but to go along with the council's action. Board President David Eaton said that teacher layoffs would not be necessary with a budget of $326 million.

"We will do everything we possibily can to maintain programs," Eaton said. It's more than it could have been, but I can't say it's full funding. I can say we are better off."

During the debate, Mason urged the council to increase the school's budget to $330 million, but later reduced the proposal to $328 million when she saw her plan was in trouble. To finance that increase, Mason proposed a 1 percent educational surtax on the income taxes paid by D.C. residents.

The council voted 8 to 4, with one absent, to reject Mason's proposal. Those voting in favor of it were Mason, Betty Ann Kane (D-At Large), Polly Shackleton (D-Ward 3), and Wilhelmina Rolark (D-Ward 8).

Mason did persuade the council to delete language from the budget bill that would have required the school board to consult with the council in the event it decides to reduce the number of teacher positions.

Council member H.R. Crawford (D-Ward 7) yesterday pushed through a variety of amendments to the budget, including one that requires the Department of Human Services to purchase emergency food stuffs that are "suitable to the population for which it is intended."

Crawford complained that poor blacks in Southeast Washington were being offered free food, including turkey eggs, stew beef, cauliflower and powdered milk, that they almost never eat. To make a point, he held up a bag of turkey eggs during the council meeting.