The D.C. City Council's finance committee yesterday voted to keep property tax rates unchanged through next June, rejecting proposals to lower rates after the city's finance director said that to do so would only worsen the District's "very tenuous" financial situation.

Carolyn L. Smith, director of the D.C. Department of Finance and Revenue, also told the committee that her agency now expects no increase in the average assessment of single-family homes in Washington next year, a result of the city's stagnant housing market.

Smith's prediction of stable assessments next year, if it holds up, would confirm a recent trend. The average Washington residential assessment increased nearly 20 percent a year ago but only 9.4 percent for the current tax year that began July 1.

Smith had earlier predicted a modest 4 percent rise for next year, but said yesterday that the forecast had been revised downward to reflect even worse market conditions than had been anticipated. "We are dealing with a recessionary economy," Smith said.

The action by the finance and revenue committee yesterday, which is subject to approval by the full council today, would mean that the average owner of a Washington home worth about $91,000 will pay about $101 more in property taxes than last year, with the average bill rising from about $900 to about $1,001, according to city officials.

James Banks, executive vice president of the Washington Board of Realtors, said the city government's forecasts indicated continued economic sluggishness in the once booming real estate market that has been severely dampened by crushing interest rates.

He said the slowdown in assessment increases could help the market slightly because "one of the big factors increasingly in sales is the amount of taxes, which have increased over the years as assessments have gone up."

Assessments, announced each spring by the city government, reflect a survey of real estate sales that took place about a year and a half earlier. Thus, unchanged residential assessments next year would reflect the condition of the housing market in late 1981 and early 1982.

The committee voted 4 to 1 against a proposal by council member Betty Ann Kane (D-At Large) to give senior citizens a tax break by freezing assessments at current levels for homeowners over 65 years of age. The bill would have cost the city about $1 million this year and about the same in fiscal year 1983, Kane said.

The committee also voted to keep the tax rate on rental property constant at $1.83 per $100 of assessed value, and the rate on commercial property at the current $2.13 per $100.

Finance committee chairman John A. Wilson (D-Ward 2) called yesterday's vote not to reduce taxes "courageous in a political year." Earlier this month Wilson abandoned his own sweeping tax reduction program that would have cost the city about $50 million over the next two years. Wilson's proposal had included a reduction of the current rate on single-family homes from $1.22 per $100 of assessed value to $1.00.

Wilson, who made the tax-reduction proposal based on optimistic economic predictions made earlier this year by Mayor Marion Barry's administration, more recently has predicted that the city will end this fiscal year with a deficit and may face tax increases in the next year.

"It's an unpopular decision, but it is a decision that has to be made," said Wilson, who has sparred with Barry about the financial condition of the city. "We should be in the posture of talking about a tax increase, not a tax deduction. But that would upset the political apple cart that's going around the city," Wilson said.