D.C. Council Chairman Arrington Dixon, raising Mayor Marion Barry's ante, yesterday proposed adding $16.2 million to Barry's 1983 budget for public schools by reducing administrative costs in selected city agencies by 3 percent.

Dixon, whose plan comes after Barry recently raised his own budget proposal for the schools by a total of $36.3 million, claimed that his further proposed increase would not result in layoffs or a reduction in public services. But Budget Director Gladys W. Mack warned that Dixon's plan would "do great violence to the budget" and almost certainly lead to layoffs.

"Based on a quick analysis, I don't think there's $16 million worth of reductions in the budget proposal without RIFs reductions in force ," she said.

Dixon claimed that the mayor's plan to spend $285.8 million on the schools next year will not be sufficient both to cover anticipated salary increases and to avert cutbacks in important education programs.

Barry originally favored reducing the school board's budget from $254 million this year to $249.5 million in 1983, in part to reflect declining student enrollment. The school board had asked for a $289 million budget.

Late last month, Barry relented somewhat by agreeing to add $14.3 million for programs and $22 million for anticipated teacher salary increases, raising the total to $285.8 million. Barry said the revision showed his support for public education.

However, Dixon noted yesterday that the school board's original request of $289 million did not include the $22 million Barry's aides now say is necessary to cover the anticipated teacher salary increases. Thus, Dixon said, if Barry's budget proposal prevails, the school board will be forced to make sharp cuts in programs to cover the salary increases.

"Despite what has been stated, the mayor's mark is still significantly lower than that of the school board," Dixon said.

To find the additional funds for schools, Dixon yesterday urged the council to support a 3-percent "administrative belt-tightening" in selected areas of Barry's overall $1.7-billion operating budget for 1983.

While most city departments would face cuts under Dixon's plan, a wide range of agencies and programs would be exempt. For example, the police department, the University of the District of Columbia and payments to D.C. employe pension funds would be spared, as well as the unemployment compensation fund, energy assistance program for low-income residents, income-maintenance and welfare programs and the repayment of loans and interest.

Mack said that Dixon's plan would undermine the mayor's efforts to offset some of the cutbacks in federal aid for jobs and housing. She also warned that the city would have to reduce spending for the fire department and corrections under Dixon's plan.