New housing sales dipped 13 1/2 percent nationwide in April, and areawide sales of new houses fell 23 percent after a surprisingly high level of sales in March, before mortgage rates rose sharply, the federal government said yesterday.

Nevertheless, sales of existing houses rose 6 percent in April across the nation after a six-month downward trend. In the Washington area, the number of resales this year has kept pace with 1980 when sales generally were depressed from the high levels of the late 1970s.

Record-high mortgage rates are expected to cause another decline in both new and existing house sales in May, after reports are tabulated.

Federal statistics released yesterday also showed that the average cost of a new house nationwide hit a record $84,000 in April, with the Northeast region at the top with $94,700 and the South at the bottom with its $76,100 average. The median price for new houses rose to a record $69,300 in April, only $800 higher than the figure seven months earlier.

Considering the recent surge of effective mortgage rates to higher than 16 percent and the difficulty of finding long-term, fixed-rate home loans, activity in both new and resale house markets has been surprisingly strong. In Northern Virginia, the Board of Realtors reported earlier that the average price of a resold single-family house exceeded $100,000 this year, a jump of $10,000 over the same period in 1980.

Housing Data Reports, which tabulates sales of new houses and condominium apartments in this area, showed new home sales up 32 percent in the first four months of this year, but that positive report was balanced by a forecast that early reports pointed to a slowdown in sales during May. Unless mortgage rates and terms become unexpectedly more attractive in June, all home sales are likely to remain sluggish here and elsewhere in the nation.

In commenting on the downturn in new housing sales in April, economist Robert Sheehan of the National Assocation of Home Builders said: "There's a real fear among builders that I haven't seen before. In 1974-75, they were mad. Now they are fearful that this thing isn 't going to get better soon enough for them to survive."

In this area, however, builders have been cautiously bullish in starting new subdivisions of moderately priced houses this year at mortgage rates "bought down" below the market level.

Jack Carlson, chief economist and executive of the National Association of Realtors, said that "a healthy recovery in home sales in not likely until mortgage interest rates recede from the current level of 15 to 16 percent."

Areawide realty patterns show resale house totals down in 1980 and 1981, with the annual rate of appreciation of resold houses also declining from a high in the 15 percent to 20 percent range in 1978-79 to 8 percent to 9 percent in the past two years.

Genrally, the slowest resale market is for homes priced from $145,000 to $180,000, the range that normally attracts persons and families moving up from lower-priced houses. Apparently, many of those buyers who already own homes are staying put to avoid higher financing costs of buying either a larger house.