Tax assessments on residences in the District of Columbia will increase an average of 4.9 percent this year, the largest average increase in four years and a reflection of vigorous sales of the city's housing, according to officials with the D.C. Finance and Revenue Department.

The increase "reflects lower mortgage rates and the resulting improved residential sales activity in the District," the department said in a statement.

Robert L. King, associate director of the department's Office of Real Property Tax, said that in past years, when mortgage interest rates were higher, wealthy and lower-income neighborhoods saw the most housing sales.

"Now the middle class is getting into it," King said.

Average assessments rose steeply in some neighborhoods, including wealthy areas and some sections that are less well-to-do, while many other areas stayed the same or increased only slightly.

The increases were announced yesterday as the city started mailing out tax assessment notices to the owners of the city's 155,060 taxable properties for the 1987 tax year, which begins July 1.

The increase for the 1986 tax year, announced a year ago, was 4.3 percent.

The increase was 1.4 percent for fiscal 1985. It fell 0.6 percent for fiscal 1984, and rose 9.4 percent for 1983 and 18.4 percent for 1982.

The biggest assessment jump for owner-occupied houses this year was in the Rock Creek neighborhood of Hawthorne, with a 16.9 percent rise.

Other sections with larger-than-average increases were Anacostia, south of Pennsylvania Avenue SE and near the Anacostia River, 10.3 percent; Barry Farms, 14.2 per- cent; Foggy Bottom, 13.4 percent, and Kalorama, 10.4 percent.

Other neighborhoods with large increases include the Kent area, in Northwest near the Potomac River with 12.8 percent; Lily Ponds, 10.2 percent; Marshall Heights, 10.9 percent; Massachusetts Avenue Heights, 10.1 percent; the Palisades, 10.9 percent; Spring Valley, 11.4 percent, and Takoma Park, 10.2 percent.

Meanwhile, a number of neighborhoods received no assessment increases, or very small ones. Neighborhoods that received no change were Foxhall, Chillum, Crestwood, Trinidad, Woodridge and Fort Lincoln.

Neighborhoods with small increases include Brentwood, 0.4 percent; Columbia Heights, 0.3 percent; Michigan Park, 0.1 percent, and Riggs Park, 0.2 percent.

The average assessment increase for the District's hotels, motels and inns was 9.1 percent, just more than one-fourth of last year's increase of 35 percent.

The year before that, many hotels and motels were hit with assessment increases of 80 percent to 100 percent.

The D.C. Board of Equalization and Review reduced many of those assessments on appeal.

This year, the average rise in assessments for rental properties was 5.9 percent, slightly higher than last year's increase of 4.9 percent.

The average increase for the District's office buildings will be 10.3 percent, less than last year's increase of 11 percent.

The average District house sale price for 1985 was $136,415, an increase of 10.7 percent over the average price of $123,235 for 1984.

As in years past, the area with the highest average single-family assessment is Massachusetts Avenue Heights, where the average assessment is $568,022.

Following Massachusetts Avenue Heights were Berkley along MacArthur Boulevard with $329,634, and Woodley with $294,482.