Mayor Marion Barry told Congress yesterday that his administration would stave off another D.C. budget deficit this year by cutting spending in the police, fire and recreation departments and other agencies and by postponing a $23.2 million scheduled contribution to the pension funds for city workers.

The mayor said he has ordered spending cuts in virtually every department under his control, ranging from $4.9 million to be saved by leaving police vacancies unfilled to $3,400 in savings through elimination of the newsletter of the Minority Business Opportunity Commission.

Other cuts will curtail job programs for out-of-school youth and adults with dependents, reduce street cleaning schedules, eliminate some purchases by the public library and close two fire engine companies.

The revised financial program presented yesterday by the mayor would balance this year's $1.4 billion operating budget, which now has a projected deficit of $59.4 million. But, he said, it would not require any new tax increase, any cutbacks in welfare or Medicaid payments and any major layoffs of city workers.

Last year, in a futile effort to avoid a budget deficit, Barry laid off more than 1,000 city workers, increased sales, commercial property and other taxes and significantly curtailed many city services.

The program of further government cuts will further erode city services that many residents and neighborhood groups complain are already inadequate. But Barry's presentation yesterday won assurance from key members of the House District Committee that they would move ahead with a bill to allow the city to sell bonds to raise $184 million in cash Barry says he must have to keep the District solvent this summer.

The package demonstrated the complexity of the city's financial situation and the fragility of the budget balance. At the same time, the proposals underscored the inventiveness of Barry's financial aides, who after a year of grappling with the budget crisis, have learned the art of moving numbers around without actually changing much in the city's operations.

City administrator Elijah B. Rogers and Philip M. Dearborn, financial adviser to the mayor, confirmed, for example, that two of the major components of the budget-balancing package -- "audit adjustments" and "pension amortization" -- will not have any impact on District operations this year.

They involve changes in accounting procedures and deferral of obligations that cut $36 million from the projected deficit without actually reducing spending.

Yesterday's hearing was arranged by D.C. Committee chairman Ronald V. Dellums (D-Calif.) to give Barry a change to assuage congressional anxiety stirred by reports that the city might incur yet another deficit this fiscal year.

The District already has a cumulative deficit of $388 million, and in asking Congress for help in dealing with it, Barry in return has committed himself to balance the budget this year and in future years.

Last week Rogers and Dearborn confirmed projections that the city would have a $59.4 milliion deficit at the end of the current fiscal year (Sept. 30) if spending continues at current rates. Yesterday Barry, Rogers and Dearborn told the committee how they expect to prevent that from happening:

City agencies will have their budgets slashed by $19 million.

Pension obligations totaling $23.2 million will be deferred to later years.

Congress will be asked to raise the federal payment for the year by $4.6 million to the maximum of $300 million.

The city will strike from its ledger $12.8 million in interest on long-term debt that is not actually due until next year -- a theoretical obligation that had been included in the deficit projection to comply with the auditing technique used by the city's independent auditors. That is a total of $59.6 million, or just a bit more than the projected deficit.

Oddly, the cumulative effect of the plans Barry presented yesterday will be to increase, rather than reduce, the amount of money the city actually plans to spend during this fiscal year.

District officials calculate that their revenues will exceed estimates by $17.3 million, and they propose to spend that much more than the $1.43 billion originally authorized by Congress.

The government will have to cut back in some programs, they reason, because welfare and Medicaid costs and this year's pension payouts to retirees -- all of which Barry has promised not to reduce -- will exceed their budgets by far more than can be covered by the additional revenue.

It is essential for Barry to convince Congress that he has brought the city's financial situation under control because he has keyed the city's future to congressional aid in the form of new borrowing authority, help on pension payments and a higher annual federal payment.

The mayor told the committee yesterday that his administration's efforts have "brought a sharp and lasting turnaround to growing deficits. The difference in just one year's time is remarkable."

None of the committee members disputed him, but Rep. Stewart McKinney (R-Conn.) warned that the "new reality" of the Reagan administration "dictates that the social programs of the 60s cannot continue to be fueled to the point where they promote unchecked and costlier growth."

McKinney said he doubted that Congress would approve the extra $4.6 million federal payment.