D.C. Mayor Marion Barry asked the City Council yesterday to approve $63.8 million in new spending for the current fiscal year, nearly half of it to pay increased costs of the Medicaid program in the District.

Gladys W. Mack, Barry's budget director, said the extra money is available primarily because the city is continuing to collect more sales and income taxes than it anticipated for fiscal year 1982, which ends Sept. 30.

That same revenue trend led to a $68.3 million surplus last year which Barry used to pay off part of the District's longterm accumulated deficit, now reduced to $309 million.

Mack said yesterday that Barry had specifically rejected a proposal that the extra revenue for fiscal year 1982 also be applied to the deficit. Instead, she said, the funds would be used for "pressing needs in people programs."

Council Chairman Arrington Dixon said the council may propose using some of the new money for other purposes, including reduction of the deficit. He said the council, which has criticized Barry's revenue and economic forecasts, will begin making its own economic forecasts with the 1984 budget, which city officials will begin to prepare later this year.

Dixon also asked Mack to give the council a breakdown on what groups are providing the extra tax revenues. "It may be time for the council to consider providing tax relief for residents who are paying more than their share of taxes," he said.

Of the $63.8 million in new revenues, Mack said $25.2 million will be used by the Department of Human Services to pay the city's cost of the federal Medicaid program. City officials said a new budget system that improved Medicaid accounting revealed the need for additional funds.

Barry initially had budgeted $40 million for Medicaid this year. For fiscal year 1983, which begins Oct. 1, the city has budgeted $93 million.

Barry also asked yesterday for an additional $5.7 million to pay for a series of unanticipated costs in the human services department, including some salaries formerly covered by federal grants, overtime at various facilities that operate 24 hours a day and additional costs connected with placing mentally retarded persons in community facilities.

Mack said $7.4 million of the supplemental budget request would be used to help cover the cost of increased wages the city negotiated with unions representing about 15,000 employes.

An additional $7.6 million was earmarked for the city school system, for pay raises and other unbudgeted salary adjustments requested by the schools, Mack said.

In addition to the $63.8 million for general operating costs, Barry also asked the council to approve capital expenditures of $774,000 to cover unexpected costs in relocating businesses and families from the new convention center site downtown.

Other requests in the supplemental budget, which must be approved by Congress, include:

* $942,000 for utility costs and renovation at the Lansburgh Building, a downtown landmark currently being used by some city agencies and city-supported arts groups.

* $100,000 for the D.C. Board of Elections and Ethics to hire temporary help and consultants to help straighten out its registration records. The administrative disarray in that office threatens to disrupt this September's primary elections, according to a City Council committee investigating that office.

* $3.5 million for the city's public housing projects to offset reduced revenues from rents and federal subsidies.

* $1.7 million to pay the federal Bureau of Prisons for the cost of keeping prisoners from the District in federal facilities. The Department of Corrections also said it needs $351,000 this year to implement changes the city agreed to in settling a longstanding suit by inmates at Lorton against the department.

* $200,000 for the Department of Licenses, Inspections and Investigations to eliminate a backlog in the issuance of certificates of occupancy,