In approving a $1.9 billion District of Columbia operating budget for the 1984 fiscal year on Tuesday, the City Council dissected Mayor Marion Barry's spending priorities and restructured them in significant ways.

Council aides said yesterday that this was the first time in the council's eight-year existence that it took a comprehensive, systematic approach to developing its own budget plan. "We went into all the agencies and control centers," said Richard C. Siegel, the council's budget director.

Aides largely credited the successful new approach to the team of Council Chairman David A. Clarke and finance committee Chairman John A. Wilson (D-Ward 2), who worked behind the scenes to rally support for major revisions in Barry's original budget proposal--including a compromise on spending for the public schools--and a new tax package.

Barry's budget director, Betsy Reveal, said yesterday she was pleased with the final version of the budget and that the mayor got "90 percent" of what he wanted. She declined to say whether the mayor would sign the bill, pending a review by the budget staff.

"By and large, we're comfortable that many, many of the things we wanted came out all right," Reveal said.

But Alphonse G. Hill, the deputy mayor for finance, saw more significant changes. He sharply criticized the council for cutting $1.2 million from the $5 million requested by Barry to cover the cost of obtaining short-term loans next year, when the city no longer can borrow that money interest-free from the U.S. Treasury.

"I don't think the council knows what it's doing when it takes out those funds," Hill said. "It doesn't understand the jeopardy it's putting the city in."

The budget contains other major departures from Barry's priorities, including:

Restoring funds that Barry wanted to cut for General Public Assistance, which aids people out of work because of disabilities; medical assistance for unemployed people who don't qualify for any other medical program, and a public school transportation subsidy the mayor wanted to limit to handicapped or needy students only.

* Cutting $3.8 million from Barry's $96 million request for funds to pay for the city government's gasoline and energy costs. Council members concluded that Barry's estimates of the city's energy needs were inflated--a conclusion hotly disputed by Reveal.

* Eliminating $2.4 million in budget authority that would have enabled the new Washington Convention Center to purchase kitchen facilities and equipment from the center's major food-service contractor.

* Scaling back about $1.3 million in spending proposed by Barry for a wide range of city agencies, including the Office of Financial Management, the Commission on the Arts and Humanities, the Office on Latino Affairs, and the Department of Environmental Services.

* Adding $5 million to the budget to help retire the city's long-term debt, which totals $296.4 million.

* Adopting a spending level for the public schools totaling $326 million, or about $7.5 million more than Barry recommended but $10 million less than requested by the schools.

The council last year added $16.5 million to Barry's proposal for the schools, but many observers said that was done primarily to curry favor with voters in an election year.

This year, the school budget was again the major issue in the council's budget deliberations. Clarke was largely credited with working out a compromise on school spending between the mayor and the council members, to ward off a strong appeal from the politically potent school lobby.

In contrast to former council chairman Arrington L. Dixon, who council members said rarely consulted with them on major issues, Clarke repeatedly conferred with his colleagues during the past few weeks on the new budget, and held three closed-door meetings last week to thrash out a final version.

Hilda Mason (Statehood-At-large), chairman of the Education Committee and a staunch ally of the school board, criticized Clarke's leadership and sought unsuccessfully to raise income taxes to give the school board more money. But several other council members, including some who had endorsed Dixon for reelection, had public praise for Clarke.