Consumer prices fell 0.3 percent in March, the first month-to-month decline in 17 years, the Labor Department reported yesterday.

One result is that the 36 million Social Security recipients will receive a 7.4 percent benefit increase starting July 1, about $27 a month for the average recipient. Because inflation has been declining, this year's increase is well below the 11.2 percent they received last year.

The White House said the March price report was evidence of "dramatic progress" in the fight against inflation. Deputy White House press secretary Larry Speakes attributed the reduction in inflation to the Reagan administration's "consistent economic policy."

The sharp moderation in consumer inflation began last year. For the last three months, consumer prices have been rising at a seasonally adjusted annual pace of 1.0 percent, according to the Department of Labor. A year ago they were rising at an annual rate of about 10 percent.

A severe recession that has reduced demand for many goods and services coupled with a worldwide oil glut and several years of good crops have combined to bring down the cost of living.

The inflation news was well-received on Wall Street, where the Dow Jones Industrial Average climbed 9.04 points yesterday.

The March consumer price index stood at 283.1 percent of its 1967 average. That means a selection of goods and services that cost $100 in 1967 cost $283.10 last month. The index was 6.8 percent higher than in March, 1981.

The abatement in inflation has been the one bright spot in an otherwise bleak economic picture. The recession has pushed the unemployment rate up to 9 percent, matching the post-World War II record set in May, 1975. Interest rates, despite the recession and the steady decline in inflation, have remained exceptionally high, although they have declined from their peaks of early 1981. Many analysts worry that unless interest rates come down, they will choke off the economic recovery that many expect to begin this summer.

Robert Ortner, chief economist for the Department of Commerce, said that, while he is "as delighted as everybody else" with the March decline in prices, he anticipates that an economic recovery will boost demand for certain goods and services and that the inflation rate will move up to its "underlying" range of 5 percent to 6 percent, roughly the rate at which labor costs have been rising recently.

John Layng, of the Bureau of Labor Statistics, said a decline in energy prices has been the major factor behind the deceleration in the cost of living, because energy is a factor in nearly all products and services.

Although natural gas prices have continued to rise because of the relaxation of price controls, oil prices have plunged as conservation and a worldwide economic slowdown have reduced demand for petroleum.

For example, gasoline prices tumbled at a seasonally adjusted annual rate of 4 percent in March, following declines of 2.3 percent in February and 1.7 percent in January. Oil-producing countries have been reducing their output recently and many analysts think that oil prices have stopped falling and may increase slightly if the economy begins to recover in the summer.

Overall food prices fell 0.3 percent in March. Fruits and vegetables were down 3.5 percent, after skyrocketing 5.5 percent in January because of severe weather and rising 1.6 percent in February.

Housing costs also fell 0.3 percent, mainly because of a decline in house prices and a decline in interest costs. Financing costs fell a seasonally adjusted 1.2 percent. Nevertheless, mortgage rates remain at near record levels.

Medical care costs continued to resist the general slowdown in consumer prices, rising 1 percent.

Despite continued high interest rates, Federal Reserve Board chairman Paul A. Volcker has said the central bank intends to keep the nation's monetary policy on the same tight track of the past 2 1/2 years to prevent inflation from rearing up again when the recession ends.

The Commerce Department's Ortner said that the Fed's policy is less restrictive than critics claim. A 9 percent growth in the money supply is restrictive when inflation is running at 13 percent, Ortner said. When the inflation rate is only 6 percent, 9 percent money growth "will accommodate a generous amount of real growth."

The annual cost-of-living escalator for Social Security recipients is based on the difference between consumer prices during the first three months of 1981 and the first three months of this year. Another 4.1 million railroad retirees and Supplemental Security Income recipients will also receive the 7.4 percent increase.