The median price of a new home built in the Washington area increased 22 percent over last year to a record $88,990, according to a report by the Metropolitan Washington Council of Governments.

It was the second year in a row in which housing prices in the area increased 22 percent. Nationally, the median sales price of new homes was about $64,100 for a roughly comparable period, reinforcing the Washington area's reputation as one of the nation's highest priced cities.

On the average, a family would require an annual income of about $35,000 to get a mortgage on an $88,990 house, according to local savings and loan officers and real estate agents.

"There's no question that as prices of houses go up, the number of people who can buy is reduced," said James G. Banks of the Washington Board of Realtors. "The challenge is to find a way to produce housing at less cost. It's not going to be easy."

The Council of Governments survey compared builders' prices for new subdivision and condominium developments as of January 1979 and January of this year.

The median sales price is the figure at which half the houses cost more and half cost less.

According to the report, Alexandria had the fewest new subdivisions -- five -- and the highest median sales price, $135,000.

It was followed by Montgomery county at $99,500, Arlington County at $98,990 Fairfax County at $97,990, the District of Columbia at $97,000. Loudoun County at $76,000, Prince William County at $73,990, and Prince George's County at $70,990.

The survey also showed that new high-rise condominiums had the highest median sales price at $138,000 and that Fairfax County had the highest concentration of new developments, 142.

Only two years ago the median sales price of a new home in the area was $60,000. Last year it rose to $72,970.

The Council of Governments survey included a total of 1,459 units in single-family attached and detached homes, new high-rise condominiums, and units converted to condominiums. The survey found that prices increased 22 percent although the average size of the model homes grew by only 7 percent.

The price increase was partly due to inflation and partly due to the decline in condominium development and an increase in the construction of single-family homes, which generally cost more than condominiums, the report said.

Information for the survey was provided by Housing Data Reports Inc., a local market research company specializing in sales of new homes.

Sales of both existing and new homes plummeted in the area, particularly in April, but began to increase again in May.

Housing Data Reports' June newsletter said sales in May increased 83 percent compared with April but lagged 16 percent behind May of last year. The sales pattern was called "spotty" -- up one week, down the next," according to the newsletter.

The median price of a new home in the Washington area is much higher than the national average. Michael Sumichrast, chief economist for the National Association of Home Builders, said the median price of new homes sold in April nationally was about $64,100, up from $62,600 a year ago.

"The increase [nationally] has been rather slow, but it's always slow during a recession," Sumichrast said.

Sumichrast said residential construction last month in the Washington area was the lowest since 1945. He estimated that only 14,000 housing units will be built this year in the area, compared with about 21,000 last year.

Sunichrast noted that many builders are trying to lure reluctant purchasers with such inducements as below market-rate financing.

Developers are able to offer such financing because large amounts of mortgage funds are often committed to their projects long before they begin selling their homes. They pay lenders a fee to keep the interest rate at relatively low levels -- a fee that, in turn, is likely to be reflected in the sales prices of the homes.

A sales agent at the complex said the purchasers of its $90,000 town houses are being offered financing at 11 1/2 percent interest, and generally need an annual income of about $35,000 a year. Mortgage loan interest rates at most institutions recently slipped to below 12 percent after reaching as high as 17 percent.

A local lending official said the purchaser of a median-priced new home would have a monthly payment of about $900 if he made a 10 percent down payment and financed his house with a conventional mortgage at about 12 percent interest. With 20 percent down, the payment would be about $800 a month.

Sales agents at some local subsidivisions say sales have been mixed, although most agree that sales have increased in recent weeks as mortage interest rates have declined.

At the Saratoga Townhomes complex in western Springfield, all but six of the 45 homes in the sixth section have been sold, according to Marjorie Morrell, sales assistant for the builder. The town houses there range in price from $85,000 up to $94,500, and two additional sections are under construction, she said.

Morrell said the homes have been sold primarily to young couples and small families, but also to some retired persons and unmarried couples.

At the other end of the price spectrum, 21 of the 26 homes in the luxury Foxhall Crescents development in the District have been sold, said Dagmar Burton sales director The huge homes there cost more than $400,000.