Tax assessments on single-family homes in the District of Columbia increased 19.7 percent in the past year, Mayor Walter E. Washington said yesterday as he proposed a program of tax relief that would ease the mounting burden on homeowners.

The now assessments reflect an average market value of $44,837 for the estimated 100,000 single-family dwelling units in the city. If this year's real estate tax rate were kept in effect, the tax bill on that average $44,837 house next summer would be $135 more than last year's, reaching a total of $711. Many bills range far higher.

At a news conference held just before the new real estate tax assessment notices are being put into the mail, the mayor said he will ask the City Council to adopt several measures that would almost totally eliminate tax increases for homeowners while permitting them to rise on commercial and rental property.

If the council were to adopt the mayor's whole package unchanged, the tax bill of $576 on the average $44,837 house would go down by $13 to $563.

Although there was only passing talk of politics during the news conference, it was obvious that the mayor hopes his program will avert a possible revolt by homeowners, many of whom feel they are being priced out of living in dwellings they may have bought years ago at low cost.

The mayor is expected to be a candidate for re-election, although he said yesterday that he has not had time to make his mind.

Two members of the council, which must pass upon the program - Sterling Tucker, the council chairman, and Marion Barry Jr., chairman of the council's Finance and Revenue Committee - have announced that they will run for mayor in the Democratic primary.

By law, the District is now required to assess all property at its full current market value - the amount a buyer would pay right now if the home were put on the market.

With the city undergoing a housing renaissance, as increasing numbers of dwellings are being bought at soaring prices and rehabilitated the assessments are constantly rising.

This was true this past year in every neighborhood in the city. Tax valuations in Barry Farms, east of the Anacostia River, with the lowest average market value in the city, increased 18.6 percent to an average of $18,212 for each dwelling. At the opposite extreme, the average home in Massachusetts Avenue Heights, just west of Rock Creek Park and including part of Embassy Row, increased 17.9 percent to $163,427 for each dwelling.

Proportionately, the highest increase in assessed values was 51.6 percent in LeDroit Park, the mayor's home neighborhood just south of Howard University. THe average valuation there is now $24,642.

In proposing his tax relief package, the mayor noted that other sources of city revenues, such as the income tax and sales tax, also are rising.

The mayor's real estate tax program is in two parts. In addition, he proposed an income tax credit for low income residents.

On real estate, the mayor proposed to reduce the tax rate on owner-occupied himes from the present $1.83 for every $100 of assessed valuation to $1,57, effective July 1.

In addition, he proposed to increase the so-called "homestead exemption" on each owner-occupied dwelling from the present $6,000 to $9,000. At the reduced tax rate, that by itself would cut the bill for each homeowner by $141.30.

The homestead exemption is simply subtracted from the assessed valuation of a home in setting the tax rate. For example, if you owe a home valued at $20,000, you would not have to pay any tax on the first $9,000 of its value. Your entire tax would be levied on the remaining $1,000.

Of the 100,000 single-family dwellings in the city, an estimated 77,000 are occupied by their owners and the remaining 23,000 are rented.

In order to take advantage of the reduced tax for owner-occupied homes, each owner would be required to fule an affidavit with the city.

The mayor did not propose a tax rate for rental or commercial properties, leaving open the likelihood that it would stay at the current $1.83.

This so-called "differential tax rate" was recommended recently by a city tax revision commission, and has been officially proposed in a council bill already introduced by Barry.

Told of the mayor's proposal, Barry said, "I'm glad to see he's got religion. His proposal [for tax relief for homeowners] is just a refined version of my own."

A spokesman for Tucker said the council chairman had not seen the mayor's proposals, and would not comment until he could read them in detail.

During the news conference, the mayor did not detail the effects that his proposals would have on the city's budget for the 1979 fiscal year, which begins Oct. 1. As usual, the proposed $1.4 billion budget is precariously balanced, and it depends upon various revenue projections that may not be met.

For example, it anticipates an average real estate assessment increase of 23 percent for this year and next.

Kenneth Gack, the city's director of finance and revenue, said the increased assessments reported yesterday would have brought in an additional $30 million in real estate taxes at the old tax rate of $1.83 per $100 of assessed valuation. The mayor's proposed relief for homeowneres would cut that by an estimated $11.4 million.

Even with the cut, the mayor said a reserve fund of $15.1 million included in the proposed budget would be preserved.

In addition to making his tax relief proposals, the mayor asked the council to approve supplemental spending requests that would add $22.6 million to the current 1978 fiscal year budget and $25.6 million to the 1979 budget. The increase eventually must be approved by Congress.

The increases are for numerous relatively small items, ranging from $175,000 to pay the cost of cleaning up after the recent tear-gas explosion at the Municipal Center office building to $1.8 million for higher snow removal costs and $7 million for higher pay for city employes.

The request for additional funds for 1978 put the city in a peculiar budgetary situation.

Congress has not enacted a formal budget for the city for 1978, and has passed a stopgap resolution that limits the city generally to continued spending at the 1977 level.

The situation arose maily because of an impasse between the House and Senate over the city's request for $27 million to start work on a downtown convention center.

The mayor, answering a question, said he has no intention of dropping the convention center request in order to clear the way for congressional passage of a 1978 budget.

Legally, however, it is apparently not possible for Congress to pass a supplemental budget for the city for 1978 if it has not passed the basic budget. Comer S. Coppie, the mayor's budget director, said the city is working on the assumption that Congress will come around to passing a 1978 budget despite the convention center deadlock. CAPTION: Picture 1, In Garfield area, which includes the 2900 block of 28th Street NW, average home assessment is $65,855, by Joel Richardson - The Washington Post; Chart, no caption, The Washington Post; Picture 2, In LeDroit Park, where these homes are, assessed values are up 51.6 percent. By Joel Richardson - The Washington Post