Mayor Marion Barry yesterday backed down from a threatened veto and signed the $1.9 billion city operating budget for fiscal 1984 that was recently approved by the D.C. City Council.

The budget, which now will undergo White House and congressional review, is expected to be brought into balance in part with a $13.5 million tax- and fee-increase package that has yet to be approved by the council.

The mayor said it was his uncertainty over the status of that package, as well as his disagreement with the council on whether it had the power to revise his revenue estimates, that prompted him to threaten last Friday to veto the budget. Council chairman David A. Clarke criticized Barry at the time for grandstanding and for discounting what Clarke said was a firm, written assurance from the chairman of the finance and revenue committee that the council would approve the tax package.

Late yesterday, Barry relented and signed the budget after conferring with Clarke and the mayor's top budget advisers.

Clarke said afterward that he was pleased with Barry's decision and was more conciliatory in discussing Barry's veto threat.

"He's very concerned as are council members, that the budget has to be balanced," Clarke said.

"It's a law that governs his conduct as well as ours, and I think the council is aware of that need."

In a four-page letter delivered to Clarke late yesterday the mayor hardly touched on last Friday's controversy over whether the budget had been legally balanced.

"I am in general agreement with the expenditure actions taken by the council and believe the commitment given by yourself and council member John Wilson . . . is sufficient to ensure a balanced fiscal 1984 budget," Barry wrote.

However, Barry said in the letter that he had some reservations about the budget, including cuts made by the council in funds for employe overtime and salaries, and reductions in funds to pay interest on short-term borrowing.

Barry said yesterday that part of the reason for his veto threat was a communications mix-up between him and the City Council over whether there were adequate assurances that the tax package would be approved. Another problem, Barry said, was that he that he had to leave town Friday to attend a conference with black leaders in Atlanta and hadn't time to talk the matter through with Clarke and Wilson.

Barry said also yesterday that he has agreed to certify the council's revenue forecasts, which include $2.5 million more in revenues from the city's lottery that he had originally estimated.

"I'm interested in moving ahead," Barry said. "We've got enough problem as it is."

The finance committee meets Thursday and is expected to approve the $13.5 million tax and fee bill, as well as $19.8 million in rate increases for the city's deficit-ridden water and sewer fund.

Council member John A. Wilson (D-Ward 2), chairman of the commmittee, apologized to Barry last Friday for delays in adopting the tax package and assured the mayor that the committee would approve it.

About $8.7 million of the $13.5 million tax package will come from an increase in the city's gross receipts tax on utilities from six percent to 6.7 percent. The six percent sales tax on utilities use will remain the same.

Barry recently abandoned a controversial proposal to boost the gross receipts tax sharply to a maximum of 11 percent on public utilities, while repealing the six percent utility sales tax.

That rise in the gross receipts tax would have been passed on to all utility consumers in the form of higher rates. It would have meant that federal agencies and nonprofit groups, currently exempt from the city's sales tax, would have had to pay part of the cost of the increased gross receipts tax.

The remainder of the tax package awaiting council action includes $2.9 million in increased motor vehicle excise taxes, $1 million in new assessments on construction in progress, $600,000 in increased corporate franchise taxes, and an assortment of other fees totaling $562,000.