The D.C. City Council yesterday rejected Mayor Marion Barry's request for permission to cut $1 million from the city's job training program this year, but a top Barry aide said the number of job training positions will nonetheless be cut.

Barry proposed the cuts as part of his overall strategy to revise District government spending and avert a potential deficit. Budget Director Betsy Reveal said Barry already has ordered the Department of Employment Services to reduce the number of slots in various year-round job-training programs from 2,760 to 2,490 and does not intend to rescind that order.

"In order to balance the budget, we have to do some underspending, and we're not going to raise the lid," Reveal said.

Even without the council's consent, Reveal said, the mayor is empowered by the city charter to order departments to underspend their budgets if he decides it is necessary to avoid an overall deficit.

Barry has proposed a total of 50 changes in spending, including the cut in job training and a $1.9 million increase in the District's operating subsidy to D.C. General Hospital.

Council members, meeting as the Committee of the Whole, yesterday voted to oppose the cut in job training. However, the council did not formally suggest where to find the additional funds to restore the slots.

"The jobs program is one of the most important that we have when you talk about an unemployment rate among teen-agers of 42 percent and an overall unemployment of 10.3 percent," said council member Charlene Drew Jarvis (D-Ward 4), chairman of the Housing and Economic Development Committee and a chief opponent of the mayor's plan.

Council Chairman David A. Clarke conceded Barry could independently underspend this year's budget for job training. But by rejecting Barry's formal request for that authority, Clarke said, "we'll be sending a very clear message that jobs in the District of Columbia are very important and that he should look elsewhere for money for D.C. General."

Council member John A. Wilson (D-Ward 2) said it was hypocritical for the council to oppose the cuts in job training without proposing alternative cuts.

However, Wilson said he intended to vote against Barry's request as a means of protesting the wholesale changes that the mayor has made in the fiscal 1983 budget that the council approved last year.

"I'll vote no just because I don't like the way the budget is being restructured," Wilson said.

Barry's plan to cut $1,046,500 from the Department of Employment Services budget would have its severest impact on job-training programs for high school dropouts and adults with dependents.

The proposal would leave unchanged a training program for high school students and a new training and retraining program for persons 16 or older who have exhausted their unemployment benefits.

In January, at the beginning of his second term, Barry pledged to mount an all-out effort to provide jobs for District residents and to get people off welfare benefits and back to work.

Also yesterday, the council members, meeting in a legislative session, gave preliminary approval to Barry's request to retain the current residential and commercial property tax rates in the coming tax year.