D.C. Recreation Director William Rumsey yesterday released a list of 21 after-school recreation centers in the city that he has recommended be closed in three weeks as part of Mayor Marion Barry's plan to avoid a $172.4 million shortage in the District budget.

The 21 centers are loacted in every area of the city except Ward 3, west of Rock Creek Park.Rumsey said no closings were suggested there because there are only two city-run after-school centers in the ward.

City Administrator Elijah B. Rogers, however, immediately decried Rumsey's action, saying that neither he nor Mayor Barry had seen the list of centers yet.

"No final decisions have been made about those 21 centers," Rogers said. "We haven't decided to close any centers at this point. When we do, it will be on an equitable basis. The mayor and I will decide, not Dr. Rumsey."

Barry, who announced last week that 21 centers would be closed as part of a $26.1 million savings package, telephoned a reporter last night to emphasize that the centers listed for closure by Rumsey were only recommendations and not yet final. "I just wanted to make sure that Bill wasn't saying something that he had no authority to say," Barry said.

The mayor said, however, that he did not believe that centers would have to be closed in all eight wards to distribute the impact of the cuts equally. "You don't have the same people in every ward that are served by each center," he said.

Rumsey's recommendations were based on statistics of daily use. Those centers with the lowest daily use were the ones recommended to be closed, Rumsey said. In all instances in which centers are closed, other centers are no more than a mile away, he said.

The city has a total of 60 recreational centers in pubic schools, as well as 65 others located in recreational facilities or public housing projects.

Rumsey listed 24 other centers that may close at 8 p.m. instead of 10 p.m. These closings were spread out among all eight wards in the District.

The purpose of closing or curtailing hours of service at the centers, is to save money paid to unionized custodial workers at the schools. "The custodial costs are just astronomical," Rumsey said.

The recreation director said City Council approval of the actions would not be necessary.

The financial plan announced by Barry on Monday contained several spending cutbacks in the area of youth affairs, including the center closings, a reduction of 800 slots in the summer jobs program and shortening of outdoor swimming pool season by one month.

In several city neighborhoods, where youth unemployment and potential idleness are high, youngsters interviewed said they were disappointed at the possible loss of facilities or shortened hours.

"We need a place for youth or else there's nothing else for them to do except be on the streets," said 18-year-old Susan Turner, a senior at Dunbar High School on Third and O streets NW.

For Lenora Gaines, 15, the recreation center at Ballou High School, Fourth and Trenton streets SE, is a place to go three times a week for dance classes, gymnastics, basketball, volleyball and Ping-pong. Without the center and others like it, she said, Washington youngsters "don't have anything to do after school."

The prospect of fewer summer jobs was a gloomy one for several youngsters interviewed, including Ballou student Gaines, who spent last summer working at D.C. Village, a city home for senior citizens, helping elderly people "thread needles, walk around and answer phones."

"I would try to baby-sit if I could, or else I might try to go to camp," Gaines said. "Probably, I'd just stay home, you know, watch TV. There wouldn't be anything to do."

Reginald Washington, a 19-year-old Ballou senior who had a summer job last year at a city-run swimming pool, said he could accept Barry's youth program reductions. "If that's the only way he can get some money back," Washington said, "then let's do it."

Reaction to the mayor's proposed cutbacks, the most sweeping curtailment of city services since home rule, was somewhat slow in coming. Many Washington resdients were puzzled because they were not sure which proposals would affect them directly.

One who was not was Geneva Grier, 60, of Anacostia, who takes care of her invlaid 69-year-old sister, Lizzie Gerald, at their 18th Street SE home. The sisters now have a city-paid homemaker who comes in four hours a day to help with chores. Without the homemaker, Grier is confined to the house because her sister is blind and in a wheelchair.

Barry proposed yesterday to freeze homemaker services at the present level as a way to make up a potential $6 million deficit in the budget of the Department of Human Services.

"We need them to come in more. We need somebody all the time because I just can't do it all," Grier said yesterday as she attended a senior citizens program at the Garnet C. Wilkinson Library on Pomeroy Road SE. c

"I don't see why the mayor would cut homemaker services," she said. "They need more homemakers, not less. It's cheaper to have a homemaker than build a nursing home, isn't it?"

Some of the largest personnel reductions would come in the Department of Corrections, where 400 jobs would be eliminated, 360 through layoffs. More than 100 of the layoffs would be made among corrections officers in all of the city's penal facilities.

Bernard Demczuk, a chief shop steward for the union representing the guards at Lorton and the D.C. jail, Local 1550 of the American Federation of Government Employees, said, "We are not going to allow the city to put our lives in jeopardy and if we have to do a job action to make people understand . . . we'll have to face it."

Yesterday, Barry began a series of meetings with citizens and special interest groups to explain the proposed spending cuts.

He is expected to announce some time this week the specifics of a $4.5 million tax and fee increase package to supplement the reductions.

Plans already outlined by Barry would eliminate 1,233 jobs from the city payroll, including 550 through layoffs. If the tax package is not approved by the City Council, Barry said, more than four times as many jobs would have to be cut.

Barry met last night with a dozen leaders of unions representing city employes, who emerged after two hours voicing concern but not militancy over the threat of job cutbacks.

Robert E. Petersen, president of the Greater Washington Central Labor Council, umbrella organization for local AFL-CIO affiliates, said a "responsible leadership" among unions here recognizes "we have a serious problem" that must be solved. He would not say outright what position the unions would take.

William Simons, president of the Washington Teachers, Union, criticized school board officals for refusing to meet with him on possible cutbacks.He said he went to the mayor's meeting to get information denied him by school authorities, and voiced hope there would be no need for teacher layoffs.