The output of the nation's factories, mines and utilities continued at a strong pace in June, the Federal Reserve Board reported yesterday.

The Commerce Department also reported that businesses added $3.3 billion to their inventories in May, a sign that the business community thinks the economy will continue to expand in the months ahead.

The Commerce Department said business inventories rose $3.3 billion in May, after a $2.5 billion April gain and a like $3.3 billion rise in March.

One of the main reasons for strong economic growth in recent months - including big increases in industrial production - has been business inventory accumulation. Some ecomonists think that businesses will feel they are overstocked in many cases and will slow their inventory orders, in turn retarding ecomonic growth.

But inventories in relation to sales are not as high as they were a year ago. In May 1977, the stock-to-sales ratio was 1.46, and in May 1976 it was 1.5.

The Federal Reserve Board said "authomotive products, business equipment and durable goods materials contributed substantially to the June advance" in industrial production.

Changes in industrial production translate directly into jobs, with rising industrial output usually stimulating factories to hire and failing production causing layoffs.

The economy has been generating mixed signals in recent months that lead some analysts to think that there will be a marked pause in economic growth. Most economists believe that while there will be a slowdown from the fast advance in the first six months of the year, the 27-month-old recovery will continue at a good pace.

Despite the strong gain in June industrial production, the unemployment rate , probably the most carefully watched of the major economic indicators, rose from 6.9 per cent to 7.1 per cent in June. But the increase occurred not because there were fewer persons at work, but because so many people joined the labor force to look for jobs.

While 270.000 persons found jobs in June, another 210.000 started looking but could not find work.

The Fed said that industrial production increased at an annual rate of 12.5 per cent in the second quarter, "after a weather-damped 5.3 per cent annual rate of increase for the first quarter."