The operating rate at America's factories, mines and utilities was unchanged in September at 81.2 percent of capacity, the highest level in three years, the government said yesterday.

The Federal Reserve said that an increase in oil and gas production offset weakness in other sectors of the economy in September to leave the overall operating rate at the same level as August.

The operating rate last month was 2.4 percentage points higher than it was a year ago. American industry has shown a steady rebound following two years of declining operating rates caused by the huge foreign trade deficits.

The 81.2 percent operating rate matches the operating level of September 1984 and is the highest since American industry operated at 81.8 percent of capacity in August 1984.

Analysts have credited this upturn to the weaker dollar, which has boosted sales of American exports on overseas markets.

But economists noted that manufacturing orders have been weak in recent months and production has shown little improvement since July, indicating that the gains in the U.S. manufacturing sector are beginning to taper off.

"After a strong burst this summer, the industrial sector has begun to slow its momentum," said Allen Sinai, chief economist of Shearson Lehman Brothers Inc. in New York.

By sector, manufacturers operated at 81.5 percent of capacity last month, off a slight 0.1 percentage point from August.

The operating rate at factories making durable goods, items expected to last three or more years, was unchanged at 78.8 percent of capacity in September. The operating rate for nondurable goods edged down to 85.5 percent of capacity, compared with 85.7 percent in August.

Most manufacturing industries showed only small changes in September with the exception of primary metal manufacturers and auto makers.

The operating rate at auto plants fell to 75.2 percent last month, down a full 2 percentage points from August as auto makers continued to reduce production in the face of high backlogs of unsold cars.