Mayor Marion Barry has asked the City Council for permission to cut $1 million from the city's job-training program this year--a 10 percent reduction in year-round training positions--and shift those funds to D.C. General Hospital.

Barry's proposal, part of an overall strategy to revise District government spending and avert a potential deficit in fiscal 1983, would reduce the number of slots in various year-round job-training programs from 2,760 to 2,490.

The mayor also proposed cutting about $900,000 from the Department of Recreation, the Human Rights Commission and the Commission on Aging, to come up with a total of $1.9 million in additional operating subsidies for the cash-strapped D.C. General.

In January, at the beginning of his new term, Barry pledged to mount an all-out effort to provide jobs for city residents and to get people off welfare and back to work. Betsy Reveal, the mayor's budget director, insisted yesterday that Barry isn't backsliding on his promise to combat unemployment, which stood at 10.3 percent in April.

Even at the reduced level of job training that the mayor has proposed, Reveal said, the District still will be assisting more unemployed adults and youths than it did a year ago.

"We would like to do more in every single program area, but we just can't afford it," Reveal said. "When you start to think about where you'll cut out $110 million in projected overspending in the government to balance the budget, some of your high-priority programs have to bear some of the brunt."

Council members Charlene Drew Jarvis (D-Ward 4) and H.R. Crawford (D-Ward 7), gave notice they will protest the proposed cutback in job training when the council's committee of the whole considers Barry's latest list of fiscal 1983 spending changes next Tuesday.

"Unemployment is the most critical problem that we face in the city today," Jarvis, chairman of the Housing and Community Development Committee, said yesterday. "If we made a commitment to provide jobs then we ought to keep that commitment."

However, Chairman David A. Clarke said the council is under strong pressure to go along with Barry's proposed "reprogramming," because rejecting it could throw the 1983 budget out of balance. Because the request is in the form of a reprogramming, the council may only accept or reject elements of the plan, not propose new ones, Clarke said.

"I don't see any reason to go along with the cut in spending for jobs , but it's balanced in such a way that we only deny it by denying the increase for D.C. General Hospital," Clarke said.

In April, Barry asked the council to adopt a supplemental budget for 1983 that, in effect, reduced the congressionally approved level of spending for the year and also shifted funds between individual appropriations titles. The council by law had the right to approve that budget as submitted or change it as council members saw fit.

At the same time, Barry sent along a packet of 50 proposed changes in spending within individual appropriations titles, including the cut in job training and the increase for D.C. General. The mayor withdrew that packet when Clarke suggested that it be included in the supplemental budget and thus be subject to revisions by the council. Now, Barry is asking the council again to approve the packet, but its form gives members little leeway to alter the mix of spending changes.

"It puts us in a tight bind," Clarke said.

Barry's proposal to cut $1,046,500 from the Department of Employment Services 1983 budget would have the severest impact on job-training programs for high school dropouts (reducing the number of slots from 790 to 430) and adults with dependents (reducing slots from 1,350 to 800).

The proposal would leave unchanged the department's training program for high school students, which currently assists 620 people, and a new training and retraining program for persons 16 years and older who have exhausted their unemployment benefits.

The department also will use local funds to employ 7,340 young people in temporary jobs this summer.

Last year, the city offered year-round job training to 2,095 youths and adults. Barry's original 1983 budget proposed 2,760 such training slots for this year, compared to the 2,490 who will be assisted if the revised budget is approved by the council.