The government's main gauge of future economic activity rose 0.1 percent in November, the smallest monthly increase since June, the Commerce Department reported yesterday.

The November increase in the index of leading economic indicators was the 10th rise in 11 months and the seventh consecutive monthly advance. The index -- which attempts to gauge economic activity three to six months in the future -- had risen 0.4 percent in September and October.

The Commerce Department said the major factor in the November increase in the index was rising stock prices. If stock prices were excluded, the indicator would have fallen 0.3 percent, Commerce said.

Although the increase in the index was much smaller than many economists said they expected, the pattern of somewhat higher increases in the past few months suggests that the economy will keep puttering along, much as it has since the summer. Much will depend on the effect of Federal Reserve Board policy on interest rates, what happens to the value of the dollar and whether consumers feel they have bought enough, according to economists.

Commerce Secretary Malcolm Baldrige said yesterday that the index has averaged a 0.4 percent increase each month in the past seven months and that "recent behavior of the leading index continues to point to moderate growth ahead."

Beryl Sprinkel, chairman of the Council of Economic Advisers, mirrored Baldrige's optimism, saying, "The trend I would view was rather strong, rising 10 of 11 months." He said that the November estimate could be revised up later. "I don't know if the 0.1 is for real," Sprinkel said.

Sprinkel yesterday released the Reagan administration's forecast of 4 percent growth in gross national product -- the nation's output of goods and services -- from the fourth quarter of this year to the fourth quarter of next year. Many economists said they expect GNP to increase at about a 2.5 to 3 percent rate. This year, preliminary estimates suggested the economy has grown at a 2.8 percent rate.

The index "points to a continuation of a slow growth pattern in the economy," said David Jones, economist for Aubrey G. Lanston, a Wall Street securities firm. The economy probably will grow at about a 2.5 percent rate during the first half of next year, Jones said. "That is probably sub par relative to where the administration wants it, but they're always too optimistic," he commented.

Wharton Econometrics is forecasting similarly sluggish economic growth for the first half of 1986, said David Berson, a Wharton economist. "We think there will be a continuation of the slowdown of consumption expenditures . . . primarily because savings are low," he said. "Individuals are going to try to build savings back up."

Economists said it is important to look at the pattern of increases in the index in the past three months and not just the small increase in November. Additionally, although some economists said that the decline in the index excluding stock prices was important, others said that higher stock prices are an important stimulant to the economy that should not be ignored.

"Stock prices do have a real effect on the economy," Berson said. "The economy is cooling, but the economy is not in imminent danger of slipping into recession."

Increases in stock prices give people greater wealth, which could lead to greater consumption. They also reduce the costs for companies to get funds for investing in new plant and equipment, because higher stock prices make it easier for companies to sell stock, and they therefore can sell fewer shares. "That also adds to total spending in the economy," Berson said.

Jones said that the Federal Reserve might try to increase economic growth by further pushing down interest rates, which would help sectors of the economy that are sensitive to changes in interest rates such as housing, construction and automobiles. This could lead to faster growth in the second half of the year, Jones said.

Additionally, lower interest rates would help push the dollar down more, which would increase the costs of imports and make exports relatively cheaper, providing a boost to American manufacturers that export by the spring, Jones said.

The indicators that contributed to the index's increase were: stock prices, net business formation, sensitive-material prices and orders for consumer goods.

The indicators that declined were: credit outstanding, orders for plant and equipment, building permits, initial employment claims and vendor performance, which gauges business activity by measuring the speed at which businesses receive deliveries from suppliers.

The average work week and money-supply indicators were unchanged.