U.S. industrial production shot up 0.6 percent in October, the best gain in three months, with a surge in auto production accounting for more than half the strength, the government reported yesterday.

The Reagan administration hailed the advance as a reassuring sign that the economy remains on track, but many private analysts discounted the figure, contending that it reflected business sentiment before the stock market collapse.

The Federal Reserve said the 0.6 percent increase followed a flat September and a modest 0.3 percent August gain. Industrial production had shot up 1.2 percent in July.

"This steady increase in industrial production bodes well for the underlying strength of the economy and for future growth," said White House spokesman Marlin Fitzwater.

Private economists agreed that the report showed a generally healthy economy before the record 508-point plunge in the Dow Jones industrial average on Oct. 19. But they said it remained to be seen whether businesses would start cutting back on production plans out of concern that jittery consumers will be less inclined to buy big-ticket items.

In a second report yesterday, the Commerce Department said business inventories shot up 0.6 percent in September while total business sales were rising 1 percent.

Economists termed the inventory increase worrisome because they expect consumer spending to weaken in coming months. A buildup of unwanted inventories can be a danger sign of an impending recession.

"There are a lot of goods on the shelf and if businesses don't get rid of them during the Christmas season, then the stage is set for a major drop in production during the first part of the new year," said David Wyss, an economist with Data Resources Inc., a Lexington, Mass., forecasting firm.

The October advance pushed industrial production 5.1 percent higher than a year ago, reflecting the gains American manufacturers have enjoyed this year because of rising export sales.

Manufacturing output climbed 0.9 percent in October. The increase included a 1.3 percent rise at factories making durable goods -- items expected to last three or more years -- and a 0.3 percent advance at factories producing nondurable goods.

Auto assemblies, which had fallen in August and September to annual rates of around 6 million units, rose to a rate of 7.3 million units in October. In addition, production of both light and heavyweight trucks increased sharply.

The industrial production report said output in the mining industry rose 0.5 percent in October, the third consecutive strong monthly gain. This category is now 5.5 percent above where it was at the same time in 1986, a year in which widespread layoffs in oil and gas exploration had severely depressed activity. Output at utilities edged down 0.1 percent in October following a 1.4 percent drop in September. The changes left industrial production at 131.7 percent of its 1977 base of 100.