The government's main barometer of future economic activity jumped 1.7 percent in January, the sharpest increase in 20 months and an indication the economy is on the rebound.

The Commerce Department's index of leading economic indicators, which is intended to forecast economic activity about six months into the future, had dropped 0.5 percent in December after several months of erratic behavior, leading some economists to doubt that the rebound from sluggish growth last fall would be very strong.

Yesterday, however, many economists said the leading indicators in January confirmed other recent government reports pointing toward relatively strong economic growth, at least for the first half of this year. Many economists are forecasting growth between 4 percent and 5 percent for the first quarter after a surprisingly strong 4.9 percent increase in the fourth quarter.

The White House, through a spokesman, said that the indicators are "predictive of healthy growth in the economy in the months ahead" and that "the economic horizon is very bright."

Commerce Secretary Malcolm Baldrige said, "After declining during the second half of 1984, the sharp pickup in January's leading index is a reassuring sign for the economy. Current data show renewed upward momentum in employment and output."

But Baldrige added a word of caution. "While the index is pointing to continued growth, the recent strength in the foreign exchange value of the dollar may have a negative influence by contributing to price declines in sensitive industrial materials and by diverting capital goods orders to foreign producers," he said.

In a separate report, the Commerce Department said that new construction put in place in January increased a robust 2 percent, from a seasonally adjusted annual rate of $318.4 billion in December to $324.9 billion. Construction of office and other commercial properties led the increase. New construction had risen 0.6 percent in December.

Many economists said yesterday that the leading indicators showed consumer demand is still very strong. However, they echoed the sentiments of Baldrige, saying that businesses and consumers may continue to buy large volumes of imports and thereby reduce domestic production.

On Thursday, the government reported that the U.S. trade deficit increased $10.3 billion in January and that the trade picture this year may even top last year's record deficit of $123 billion.

On the positive side, economists said that homebuilding and automobile sales have picked up strongly, and consumers' incomes, employment and confidence all are increasing.

However, one of the key leading indicators -- contracts and orders for plant and equipment -- declined in January following erratic changes in the previous several months. In addition, another government statistic measuring new orders for nondefense capital goods plunged sharply in January and has been weak in recent months.

Some economists such as David Jones of Aubrey G. Lanston & Co. Inc., a securities dealer, said that the unveiling of the Treasury Department's tax reform plan last November could have made businesses uncertain concerning the tax effects of their new purchases.

In addition, Jones said, many businesses are purchasing equipment from foreign suppliers, which, because of the rising value of the dollar, are able to offer less expensive capital goods.

The indicators provide "other evidence that we're starting the year on a solid note," Jones said.

One of the strongest positive showings in January was the 8.1 percent jump in new orders for consumer products and materials, which covers industries accounting for more than 40 percent of industrial production, Baldrige said. That category has inched upward in recent months.

Other indicators that were positive in January were change in credit outstanding, money supply, stock prices, net business formation, building permits, average weekly initial claims for state unemployment and vendor performance, which measures the demand of businesses for goods based on the speed with which companies receive deliveries. The other indicators that were negative were change in sensitive materials prices and the average work week.