Industrial production rose 1.1 percent in May, much less than April's exceptionally strong 2 percent increase but nevertheless an indication the economy is expanding swiftly, the Federal Reserve reported yesterday.

Production gains were widespread among materials and products, with the largest increase coming in durable consumer goods, which climbed 2.4 percent in May. Autos, a major part of that category, were assembled at an annual rate of 6.2 million units, up from 5.9 million in April.

The Federal Reserve said that current auto industry production schedules suggest a sizable further increase in assemblies for June. New car sales have been running above production figures for some time, encouraging manufacturers to continue raising their production schedules.

The May rise in the industrial production index, which measures the output of the nation's factories, mines and utilities, was the sixth monthly increase in a row. The index is now 7 percent above its low last November but is still about 6 percent lower than in mid-1981, before the recession began.

Jerry Jasinowski, chief economist of the National Association of Manufacturers, said the latest industrial production figures "show a continuing trend of a stronger and broader recovery. The second quarter could show real economic growth in the 6 to 7 percent range.

"It's clear that we are talking about a much stronger recovery for the next two or three quarters, although there are serious questions about its strength beyond that point," Jasinowski said.

Forecasters have been revising upward their estimates of how fast the gross national product, adjusted for inflation, will rise this quarter, and most now consider a 6 percent rate to be the minimum that is likely. Robert Ortner, chief economist at the Commerce Department, believes that the increase in production needed to halt the reduction in business inventories alone could account for a 6 percent rate of gain in real GNP.

The demand related to the swing from cutting inventories to increasing them should also give a boost to GNP in the third quarter, as will continued gains in consumer spending. But most forecasters--Wharton Econometric Forecasting Associates is a major exception--believe the recovery's pace will slacken as the year progresses.

Economists had said the industrial production index likely would not continue to go up as fast as it did in April. That month's increase, originally estimated at 2.1 percent, was the largest in eight years. While the April figure was revised downward slightly, those for February and March were each raised by 0.1 percentage points, to a 0.5 percent and 1.3 percent increase, respectively.

With the exception of consumer durables, the May increase in every major industrial production category was smaller than the month before. The smallest increase was in nondurable goods for consumers, which went up 0.3 percent compared with 1.4 percent in April. Even among consumer durables, production of "home goods" such as furniture and appliances went up more slowly than the month before.

Among other final products, production of business equipment rose 1.7 percent. Production of building and mining equipment rose sharply as a long series of declines ended in oil and gas drilling and the lengthy strike by workers at the Caterpiller Tractor Co. was settled, the Federal Reserve said.

Similarly, output of defense and space goods in the final products group rose by 1.3 percent. Large increases in defense spending led to a 12.3 percent increase for the category in the 12 months ended in May.

Over the year, the only larger increase was in construction supplies, where a continued high level of office construction and the recovery in new home building have together raised demand to the point that prices for many types of construction supplies have risen sharply in recent months. Production was up 14.2 percent for the year, though the May rise of 1.9 percent was the smallest for any month in 1983.

Output of materials, such as steel and nonferrous metals, paper and textiles, increased 1 percent compared with 2.1 percent in April.