The nation's industrial production last month rose 0.9 percent, the second smallest increase this year, but enough to suggest third-quarter real growth will remain strong.

Economists predicted yesterday that the pace of industrial production should continue through next year, further reducing the unemployment rate.

The rise in factory output is still outpacing consumer spending because businesses are attempting to rebuild inventories that were depleted during the recession.

The August increase--subject to later revision when all data is in--compares with revised advances of 2 percent in July and 1.3 percent in June.

The Federal Reserve Board reported that the increases in output were widespread among products and material, and sharp gains were noted in the home-goods and construction-supplies industries.

Many economists had expected factory output to increase at a somewhat slower pace than it did in August, although many still expect expansion to increase through 1984, suggesting that the job market will continue to grow. More than 1.5 million people have found work in the last four months.

In a separate report, the Labor Department said 409,000 persons filed first-time claims for government unemployment benefits during the week ending Sept. 3. This was the smallest number to seek benefits since early August. The number of unemployed people seeking benefits dropped by 5,000 from the previous week, which itself showed a decrease of 22,000 from the week before that, the Labor Department said.

Although retail sales and automobile sales have slowed recently, production should still increase because of the inventory buildup, said Robert Scott, economist with Chase Econometrics Associates Inc. Growth in factory output should remain about the same in the coming months, he said.

"Continuing rapid gains in industrial production this month suggest that the third quarter will witness real growth in the 8 percent range, comparable to the second-quarter performance" in which the GNP rose at a 9.2 percent rate, said Gordon Richards, director of economic analysis for the National Association of Manufacturers.

"During the second quarter, the recovery was driven primarily by a surge in spending, and inventories fell to historically low levels," Richards said.

The ratio of inventories to sales increased slightly in July and, he said, "the August gains in production, combined with a minor drop in retail sales, will result in some rebuilding of stocks. The process of inventory rebuilding should produce continued rapid industrial growth until the middle of next year."

In 1984, the recovery is expected to be driven by business investment, rather than consumer demand, which is credited with starting the economy's rally earlier this year.

Output of automobiles and steel increased modestly after surges in July.

Industrial production last month increased 11.6 percent compared with last November, which was the trough of the recession. According to the Fed, the nation's industries have recovered 80 percent of the decline in output since July 1981, when the recession began.

Output of consumer goods increased 0.6 percent, after a sharp increase in July. Production of home goods "continued to increase rapidly, led by a further increase in household appliance output," the Fed said. Nondurable consumer production rose 0.3 percent.