The District is considering imposing for the first time a fee for use of the city's tennis courts, swimming pools and other facilities now provided to residents without charge.Such a move is seen as a means of meeting rising costs for city recreation programs.

William H. Rumsey, director of the D.C. Recreation Department, told a reporter yesterday that if the City Council passes legislation that would allow his department to charge fees for services and use of facilities, that some such fees could be imposed by the fall of 1978.

Rumsey announced his fee study - which he said the Senate directed him to make earlier this year - at a City Council budget hearing yesterday after committee chairman William Spaulding (D-five) asked him whether the Recreation Department had ever considered such charges.

Recreation officials had told Spaulding's committee on education, recreation and youth affairs that unless they got more than $450,000 over what the department is asking in the 1979 city budget, that the present level of services would be reduced.

Rumsay said that because of the department's budget crunch for 1978, 11 small neighborhood recreation centers, most of them in elementary schools, will have to close or sharply reduce their scheduleds. The staff, money and equipment from the smaller centers will be used to help staff and equip six new and larger facilities.

The centers that will close are in Seaton, Morgan, Slove, Noyes, Bryan, Tyler and Logan elementary schools and Cardozo High School. Centers that will operate at reduced hours are in alle, Garrison and Harris elementary schools.

The six new centers will be in Reed, Terrell and Wilkerson elementary schools; Fletcher Johnson School, which combines elementary and junior hight classes; at Shaw Junior High and Dunbar Senior High.

Rumsey said the study's initial findings show that the city could receive "as a very rough guesstimate" about $900,000 excluding overhead costs from swimming pool fees alone. But he said that it was "too early" to tell how much user fees for tennis courts, admissions charges to park concerts and plays and other services could bring in.

Under one fee plan being considered, families, regardless of the number of members, could be charged as much as $100 a year to use swimming pools, and senior citizens may charged a reduced rate of $15, Rumsey said.

Individual pool rates could be 50 cents for age 12 to 17, and free to children under 12.

The department is considering a $5-a-week tennis court charge for four one-hour sessions, or $2 an hour for daily use. Rumsey said he is considering fees for tennis lessons as well. Abortion Funding

When Health, Education and Welfare Secretary Joseph A. Califano announced an end to federal funding of abortions earlier this month, the District decided to use about $2 million in city tax money to pay for the procedures.

The decision by city officials was hailed by proabortion groups at budget hearings yesterday on money requests for the Department of Human Resources, which administers the abortion program. But the decision was characterized as "most appalling" by groups opposed to abortion.

Deborah Menke, acting chairperson for the Abortion Rights of Washington, told the committee:

"Teen-age mother have the dimmest prospects of succeeding in our society. Early pregnancy more often than not results in incomplete schooling, broken marriage, poor employment prospects and continued welfare dependecy, Abortion can provide a very real opportunity for young, poor women to break out of the vicious cycle of poverty."

Terrence M. Scnalon o f the D.C. Rights of Life Committee, said that "this is an issue of human beings - not just women's issue; not just a preborn child's issue; it is an issue of whether a society shall be good or corrupt."

Albert Russo, director of the city's human resources agency, said $2 million in city tax money would be spent to pay for an estimate 7,500 to 10,000 abortion expected to be performed in the District during the next year. Mayor's Office Budget

Abandoning what some of his colleagues said had been a "gentlemen's agreement," City Council member Arrington Dixon yesterday proposed some key cuts in a proposed $36.3 million 1979 operating budget for the mayor's office.

Among other things, the reductions would halve the staffs of the city's Public Information and Management Improvement offices, and the Office of Municipal Audit and Inspection.

They also would force the major's new general assistant, former Department of Human Resources director Joseph P. Yeldell, to fill three jobs on his personal staff from already existing - but occupied - positions elsewhere in city government.

An addition, Yeldell would be denied a request to transfer to his office seven additional positions to assist him in examing management efficiency throughout city government.

"What is essentially being requested is a severe emasculation of the mayor's capability to effectively manage the executive branch of government," said budget director Comer S. Coppie.

Dixon's proposal came as the City Council's government operations committee, of which he is chairman, began to mark up the proposed $1.3 billion city operating budget for the fiscal year beginning Oct. 1, 1978.