Mining output, which includes oil production, rose 0.2 percent, its sixth straight increase.
Factory output is the largest component of industrial production. It had shown signs of rebounding over the summer, raising hopes that factories would help drive economic growth in the second half of the year.
But several reports suggest businesses and consumers had both grown more cautious right before the 16-day partial government shutdown. And overall hiring has slowed. Those factors could keep the economy weak until next year.
Orders for industrial machinery and other core capital goods, which signal business confidence in the economy, fell sharply in September, the government said last week. Economists pay close attention to those orders because they typically signal expansion.
Still, one measure of manufacturing said overall factory activity expanded in September at the fastest pace in 2 ½ years. The closely watched Institute for Supply Management manufacturing survey noted that production rose and manufacturers stepped up hiring, while new orders jumped, though not as quickly as the previous month.
Some economists see that as a sign manufacturing may yet pick up later this year or in early 2014.
"With a modest global recovery underway and the dollar now falling, we would expect industry to perform a bit better," said Paul Ashworth, an economist at Capital Economics.
A measure of the total existing capacity used by factories, mines and utilities rose to the highest level since July 2008. That suggests that if demand rises much more, companies will have to invest in more factories and other production facilities to increase output.
The Fed's gauge of capacity utilization is still about 2 percentage points below its 40-year average of just over 80 percent.
The Fed's report on industrial production was delayed by the 16-day shutdown. It was originally scheduled to be released Oct. 17.
Most economists predict growth slowed in the July-September quarter to an annual rate of about 1.5 percent to 2 percent, down from a 2.5 percent rate in the April-June quarter. And the shutdown is likely to keep growth at that sluggish pace for the final three months of the year.