Housing construction in the United States slipped slightly last month to a seasonally adjusted rate of 1.611 million units, but the total number of starts remained high enough to complete the best first quarter since 1979, the Commerce Department said yesterday.

The improvement over last year's rate continued to be dramatic, as it has been since January. The rate for this March increased 75 percent over March 1982's, and the total for quarter was up 82 percent over that for 1982's first quarter.

Despite the 9 percent decline from the February rate of 1.775 million starts, "The March housing starts rate is still a good number," said Harry Pryde, president of the National Association of Home Builders. "We were expecting the March decline because the production numbers for January and February were inflated slightly by seasonal adjustment factors."

Likewise, Mark Riedy, executive vice president of the Mortgage Bankers Association of America, termed the rate "a decent-looking number" and said he was "not at all discouraged" by the slight decline. "When you have a housing recovery this strong, the numbers are bound to bounce around a bit."

Jack Carlson of the National Association of Realtors agreed that a decline was to be expected.

"The starts rates in January and February reflected a surge of initial activity that could not be sustained. Even so, the March rate is very respectable for this stage of the housing recovery," Carlson said.

All three men pointed optimistically to the rate at which new building permits were issued last month. The Commerce Department put that figure at 1.434 million, down 4 percent from February but up 69 percent from March 1982.

"That means in April and May we'll see numbers like the first quarter" for starts, Riedy said.

Pryde noted, however, that NAHB is finding that many builders were starting units in anticipation of a further decline in mortgage interest rates, and that, "If interest rates don't decline another point or two, we could get stuck with a large inventory of unsold new homes in certain areas of the country."

Meanwhile, Federal Reserve Board economists said yesterday that widespread improvements, led by the steel and oil industries, helped the nation's factories increase production in March to 69.4 percent of capacity, the busiest pace in eight months, United Press International said.

The overall gain of 0.7 percentage point came largely the result of the housing boom and occurred despite a drop in the auto industry's operating rate to 58.8 percent of capacity, UPI said.

An NAHB spokesman said a survey of builders indicates that more than half foresee a "good to excellent" market for detached single-family homes in the next six months. "You have to go back to 1978 before you get a response that positive," the spokesman said.

Riedy said, "I don't know that we'll get a point or two decline in interest rates , but a half point is not out of the cards, maybe a whole."

He said he doesn't expect much more of a decline in the FHA and VA rates, but he does look for further cuts for conventional loans. He said the new types of accounts that savings and loans can offer are drawing in large amounts of cash, and the institutions "can't get the money out fast enough."

As a result, many are going back into conventional, fixed-rate mortgages at very competitive rates. "The danger to that is that, if rates go back up, the mortgages could be under water. But inflation looks good still. There is no reason to expect a dramatic worsening. I expect we'll bump along at about 5 percent, give or take a point" at least until next year when the effect of the "horrendous" deficits is likely to be felt, Riedy said.

"Housing is going to enjoy itself for a year," he said.