The Washington area continued to lead the nation last year in the price of existing houses, year-end statistics show.

In the last quarter of 1976, the average price of a single-family house here was $66,900 (compared with $54,000 in Atlanta), while new homes were averaging $58,000, the fifth-highest average in the country. (San Francisco had the most expensive new housing nationally and was second-highest for existing homes, which averaged $60,800.)

In the number of building permits issued for future housing, the Capital area far outran last year's national increase of 36 per cent. Here, permits for all types of housing were issued for 17,899 units, a 93 per cent climb over the previous year's 9,821 and better than the 16,887 permits issued in 1974. The figures were compiled by Michael Sumichrast, chief economist for the National Association of Home Builders.

Activity was strong during the normally slow months of November and December, Sumichrast said. In December, permits rose 7 per cent over the previous month, to a level that was the highest for any December in four years.

In the District, however, it was the most active December in terms of permits since 1960. There, permits for 385 units for housing were issued, all but four for federally subsidized apartments. For the area as a whole, some 20 subsidized apartment projects are currently in the pipeline.