The Commerce Department said yesterday that its chief barometer of future economic activity fell sharply in January, but an upward revision of December's showing eased fears that the nation was headed for a recession.

The department's index of leading economic indicators dropped 0.6 percent in January. Analysts discounted the decline and instead focused on a revision that changed the index's showing in December from a 0.2 percent decline to a 0.3 percent increase.

The upward revision for December broke a string of three consecutive monthly declines, which has often in the past been the signal of an impending recession. The index had fallen 0.1 percent in October and 1.1 percent in November.

The leading index has taken on added importance since Oct. 19, when stock prices plunged a record 508 points. Economists said the December revision in the leading index and other positive signs provided evidence that the country is suffering few adverse effects from the market turmoil.

"The leading index shows that this is a no-recession year for the U.S. economy," said Allen Sinai, chief economist for the Boston Co. "The magic string of three or more declines, which has often suggested a recession, was broken."

Since it was created in 1948, the leading index has fallen three or more months during an economic expansion on 12 different occasions. On eight of those instances, a recession did follow. But four times the index gave a false signal of a downturn and the recovery kept going, although at a slower pace.

Analysts said the index is sending a signal of slower growth for the first half of 1988, but they predicted that rising export sales would be enough to offset expected weakness in consumer spending and construction.

In one indication that the economy has slowed, the Commerce Department said in a second report yesterday that construction spending fell a steep 2.9 percent in January to a seasonally adjusted annual rate of $395.2 billion. It was the biggest drop in 10 months and reflected widespread weakness in all categories of construction.

Three-fourths of the decline in the January leading index came from an increase in new claims for unemployment benefits, which averaged 351,000 a week in January, an increase of 39,000 weekly claims from December. Since January, however, weekly unemployment claims have been falling, further easing recession fears.

In all, five of the nine available indicators showed weakness during January. After unemployment claims, the biggest negative factors were a drop in building permits, a decline in manufacturers' orders for consumer goods, changes in raw materials prices and changes in business delivery times.

Four indicators showed strength during the month, with a rise in stock prices making the biggest gain. Other positive forces were the growth of the money supply, increases in the length of the average workweek and a rise in orders for manufacturing plants and equipment.

The various changes left the index at 190.2 percent of its 1967 base of 100.