The economic recovery continued at a robust pace in June as industrial production increased 1.1 percent, the fourth straight month of major gains, the Federal Reserve Board reported yesterday.

Durable consumer goods--especially automobiles--led the increase in output, although gains were noted in all sectors of the nation's factories, mines and utilities. The largest gain so far this year was a 1.9 percent increase in industrial output in April, and economists said identical output gains in May and June showed that the recovery was still strong.

In a separate report, the Labor Department said that the Producer Price Index for finished goods rose 0.5 percent in June, a jump from the 0.3 percent increase reported in May and representing an annual rate of 5.6 percent. The index dropped 0.1 percent in April. The price increases, led by higher energy costs, are not an indication of a new round of inflation, economists said yesterday. The level of inflation should remain moderate--at about 4 percent--for about a year, they said.

The White House reacted positively to news that industrial production had risen for the seventh straight month. "The robust recovery continues on a broad front," said spokesman Larry Speakes. He called the increased output and moderate price increase "a winning combination" that shows inflation is still under control while the recovery is underway.

Jerry Jasinowski, chief economist for the National Association of Manufacturers, said the recovery "is now becoming broadly based as the recessed durable manufacturing sectors have come back. The rapid growth in consumer durables--autos, home goods and construction materials--are particularly significant, reflecting both renewed consumer confidence and looser credit conditions."

The increase in industrial production is about typical for a postwar recovery, according to the Fed. Output in the second quarter was more than 4 percent higher than that in the first quarter, and the index for June was 8.2 percent more than that in November 1982, when the recession was at its worst. It was 5.2 percent higher than in June last year.

Automobile production and higher output of goods for the home led the 3 percent increase in durable consumer goods in June. Production of home goods--appliances, air conditioners, televisions, carpeting, furniture and miscellaneous goods--generally increases along with an improvement in housing sales, another indicator of economic recovery. Consumer goods increased 1.2 percent last month and 4 1/2 percent over output in June last year.

Output of business equipment rose 0.8 percent in June. Construction supplies production increased 1.7 percent over May and 14 1/2 percent over June 1982. Mining and utilities activity increased 0.4 percent over May, but it decreased 3.4 percent from the same time last year. Manufacturing production increased 1.1 percent from May to June, and was 6.5 percent higher than the previous June.

The speed of the recovery was reflected in the rise in wholesale prices, which may induce fear of inflation in some people's minds and is "not quite as good a report as industrial production," said Robert Ortner, the Commerce Department's chief economist. But he said the increase in wholesale prices "is not a fearsome report."

Ortner said that inflation should remain moderate at least for a year, because the economy has plenty of room for growth, and increased consumer demand can be met by production rather than showing up in higher prices. He also said that wage increases have moderated, reducing inflationary pressures.