D.C. City Council member and mayoral hopeful Marion Barry proposed yesterday a $16 million plan aimed at cushioning the financial impact next year of rising rents of property tax assessments on Washingtonians.

The two new major proposals made by Barry yesterday were for a reduction of 13 per cent in the city's current property tax rate, from $1.83 to $1.59 for each $100 of assessed value (for residents only), and an extension of the income ceiling for the "circuit breaker" tax credit program from $7,000 a year to $20,000 a year.

The $1.83 tax rate would remain effect for commerical properties in the city.

Barry's proposal would establish a two-tier tax rate structure with commerical properties being taxed at a higher rate than residences. The plan would accomplish this without raising the tax rate for businesses. A proposal that would have allowed such tax rise was fought by the city's business community and, with the assistance of Barry, was rejected by a Council committee last month.

Barry also proposed continuation of the present program that exempts the first $6,000 of assessed value of all residential properties when property taxes are calculated.

Because the circuit breaker plan limits the amount of tax relief based on family income, it was difficult yesterday to determine an average amount that could be saved by a "typical" city resident.

But under Barry's proposed circuit breaker tax relief extention, a family with an income of $4,000 that is paying $150 a month in rent would recieve an increased tax credit from $135 to $207, while the tax credit increase for a family with a $8,000 income would go from $32 to $180.

A family whose income is $12,000 and pays $250 a month in rent currently receives no tax credit, but could be eligible for a $81 credit next year. A family with a $17,000 household income paying $400 in monthly rent would receive a $36 tax credit.

However, Barry said the overall goal of the tax relief and rent cost increases equal to general rises in the cost of living in Washington , which Barry projected would be about 5 per cent next year.

"No one objects to paying what is normal inflationary growth," Barry said.

Many city homeowners have been alarmed during the past two years because residential property tax assessments have gone up on an average of about 37 per cent.

Barry's plan assumes that assessments would increase by at least 18 per cent and perhaps as much as 28 to 30 per cent. Barry acknowledged yesterday that his effort will not actually reduce tax bills below their present levels. But he pledged, however, to seek legislation that would return to taxpayers all monies collected from property taxes that totaled more than the calculated cost of living increase.

The tax package was announced at a press conference, complete with large cardboard charts, and at its conclusion was applauded by a few members of Barry's staff. The proposals came at a time of heightening political activity and continued budgetary uncertainty in city government.

Barry already has announced that he plans to begin a campaign for mayor early next year. One of his likely opponents is expected by City Council Chairman Sterling Tucker, who last week announced a proposal for a $10 million rent subsidy program.

Both Barry's and Tucker's plans rely on partial funding from a proposed $15.1 million reserved fund established by the City Council when it tentatively reduced Mayor Walter E. Washington's proposed 1979 operating budget.

However, Mayor Washinggton, who also is a possible candidate for mayor in 1978, is to act on the budget next week, and is almost certain to veto some of the reductions proposed by the Council, thereby chipping away at the reserve fund on which Barry and Tucker hope to draw. Tucker already has said that some of the votes anticipated may be sustained.

Barry said, nevertheless, that he felt funds for the program could be found somewhere in the city's coffers. "I don't have mayor responsibility to find everybody's money in the city," Barry said, "but I've found enough for this program .