The nation's industrial output rose 0.6 percent in December for the strongest increase since July, reinforcing hopes that the economy is on the verge of a modest rebound.

The average industrial production rose 11 percent last year and, after a sharp slump in September and October, output has increased strongly, the Federal Reserve Board reported yesterday.

The Commerce Department reported separately, however, that retail sales declined 0.1 percent in December, following a 2.0 percent rise in November. Sales last year were 10.4 percent above those in 1983. But consumer purchases appeared to be on the upswing after the third-quarter slump, as the last three months of the year showed a pickup in retail sales.

An unusual decline in spending for automotive products pulled down sales for December, the Commerce Department reported. Excluding those purchases, retail sales rose 0.5 percent in December, and department stores posted a 2.3 percent gain.

Economists said the two reports, combined with other statistics showing low inflation and slowly rising employment, present a picture of an economy still in flux. Many economists said they expect consumer spending to pick up in 1985, in part because of declining interest rates, increased employment and rises in incomes, although consumer activity will rise at a slower pace than in the beginning of 1984. "It's sort of a mixed bag," said Steven Wood, an economist with Chase Econometrics. "It looks like we'll be sitting here in the ho-hum stage a bit."

Commerce Secretary Malcolm Baldrige said that sales increased at an annual rate of 10.5 percent in the fourth quarter, following a decline of 3.4 percent in the third.

"This pickup indicates that spending has resumed its upward course," Baldrige said. "Continued growth in incomes indicates another good year ahead for retail business, but gains will be slower than in 1984."

Retailers had hoped for a large increase in sales during the Christmas season to help their profits. However, although volume may have picked up in the holiday buying season, many retailers had to slash prices to reduce inventories, resulting in the low value of December sales.

Despite the drop in total dollar sales, the volume of department store purchases rose 2.3 percent in December, following a 3.3 percent rise in November. Economists also said the December retail sales figures were pulled down by a 2.3 percent drop in automotive sales.

"The sales number was peculiar" because unit car sales actually advanced in December, Wood said. He speculated that the cars that were sold were smaller, lower priced models and that the automotive sales figures also included used cars and parts.

Total sales for 1984 were $1.3 trillion, 10.4 percent higher than the 1983 total.

"On balance, after the summer doldrums, the consumer area has picked up again and can be expected to grow along with growth in incomes," said Robert Ortner, the chief economist at the Commerce Department. He said, however, that the growth in consumer spending could be offset if consumers satisfied their pent-up buying demand last year. Consumer spending is expected to slow to a 3 to 3.5 percent rate after a 4.2 percent rate last year.

Durable goods sales declined 0.9 percent in December. Automotive sales declined for the first time in four months, although they rose 6.1 percent compared with a year ago, Commerce said.

Furniture sales rose 2.8 percent in December, the fifth consecutive month of increases. Holiday sales were strong in electronics, Commerce said.

Nondurable-goods sales rose 0.4 percent in December and were 7.4 percent above sales in December 1983. Food store sales dropped 0.9 percent in December, and apparel and eating and drinking sales rose about 1 percent in December, 11 percent higher than a year earlier, Commerce said.

The Federal Reserve report said that the production of consumer goods rose 0.6 percent in December.

Durable-goods production increased 0.8 percent, and nondurables production rose 0.5 percent, the Fed said.

Automobile assemblies rose at an annual rate of 8.1 million units from a rate of 7.9 million in the previous month.

Production of goods for the home increased 0.5 percent last month, and business equipment output rose 0.7 percent.

Manufacturing output increased 0.6 percent, following a 0.4 percent rise in November.

Mining output increased 1.0 percent in December, following a 1.3 percent increase the previous month.

Utilities production declined 0.9 percent in December, following no change in November.