The nation's industrial output edged up in December following slight declines in the two previous months, the government reported yesterday, reflecting slowdowns both in autos and in other key industries.

New figures published by the Federal Reserve Board showed production in factories, mines and utilities rose 0.3 percent over the month, offsetting a similar-sized decline in November and an 0.1 percent dip in October.

At the same time, the inventories of American businesses rose 0.7 percent, or $2.95 billion, in November to a seasonally adjusted $424.16 billion. Stock building jumped 0.9 percent the previous month.

The figures on industrial output were in line with most current forecasts, which predict a visible slowdown in the first and second quarters of this year, followed by a lackluster recovery.

The economy has been providing mixed signals in recent weeks, with some indicators -- such as employment and retail sales -- showing that substantial strength still remains and others pointing to new weakness.

The rise in industrial output was dampened partly by the slump in the auto industry. Auto assemblies fell to a seasonally adjusted annual rate of 6.8 million units, down from an already low 7.2 million in November.

Major U.S. auto companies had shut down several key plants last month to help ward off a further glut in inventories, but apparently reopened them briefly just before Christmas.

However, the Fed said yesterday early signs pointed in auto production in January, and analysts said there was some possibility the layoffs might spread to related industries as well.

The report showed that output of business equipment rose one percent in December after an 0.2 percent jump in November. Production of consumer goods edged up 0.1 percent after an 0.5 percent dip the month before.

Meanwhile, output of materials rose 0.1 percent in December, following an 0.5 percent drop in November. The overall index stood at 152.2 percent of its 1967 average in December -- a rise of 0.3 percent from a year ago.

The 0.7 percent rise in business inventories was not regarded as particularly troublesome. Manufacturers' stocks rose 1.2 percent over the month, while inventories of wholesalers declined 0.2 percent.

The closely watched ratio of total business stocks remained at 1.42 months in November, virtually unchanged from the previus month's level. If the ratio were to climb sharply, it could mean excess accumulation. l