The government's main barometer of future economic activity rose 0.3 percent in October, indicating continued modest growth in 1986.

The index of leading economic indicators -- which purports to gauge economic activity within about three to six months -- has risen every month this year except April after falling on balance during the last half of 1984, accurately predicting the economic slowdown during the first part of this year.

Commerce Secretary Malcolm Baldrige said that the increase in the leading indicators in the last six months "is consistent with the recent pickup in overall economic growth. While some cross-currents in output and spending are evident this quarter, the leading index is pointing toward continued expansion in 1986."

The Reagan administration forecast an economic expansion of 4 percent in 1985 and is counting on growth of about 4 percent next year as well to prevent the federal budget deficit from rising and to lower the unemployment rate below 7 percent. So far this year, the economy has grown at about a 2.2 percent rate, however, although from July to September the pace was at a 4.3 percent rate.

Many private economists said yesterday that they expect the economy to grow at a rate between 2.5 and 3 percent next year, with continued relatively low inflation. Additionally, declining interest rates should help bolster the housing industry, economists said.

In a separate report, however, the Commerce Department reported that new housing sales dropped 6 percent in October. Sales of new one-family homes have dropped steadily since August and last month were at the same level as in October 1984. Commerce cautioned that it takes about four months to establish a trend for new houses sold. The median sales price was $96,200 and the average price was $102,700 in October.

Baldrige said that in the last six months the leading indicators index has increased an average 0.4 percent. "Past relationships show that average gains of 0.5 percent per month in the leading indicators are consistent with next year's target of 4 percent growth" in inflation-adjusted gross national product -- the nation's output of goods and services -- Baldrige said.

Private economists also said that the leading indicators suggested sustained growth next year, but at a slower pace than that predicted by the administration. For example, Allen Sinai, chief economist for Shearson Lehman Brothers, said, "The small rises on average suggest the pace of economic expansion will be relatively slow, from 2.5 to 3 percent, in 1986."

The leading indicators index, "in my view, does not support more optimistic reports on the economy for 1986" such as the 4 percent growth forecast by the administration, Sinai said.

Edward Yardeni, economist for Prudential Bache Securities, said that the leading-indicators index "suggests that the economy is in no danger of sinking into a recession, that the economy continues to grow but in a fairly lackluster fashion. The economy is neither about to boom nor about to bust."

Although growth will only be about 3 percent next year, Yardeni said, such a modest pace is not necessarily bad. "As long as we can keep this kind of nice leisurely cruising speed in the economy, it can be a fairly long-lasting expansion" with low inflation, Yardeni said. Some sectors of the economy are not doing well, but generally the economy "is not too shabby," he said.

Six of the 11 indicators available in October contributed to the index's increase, the Commerce Department said. They were: change in credit outstanding, average weekly initial claims for state unemployment insurance, change in sensitive materials prices, stock prices, manufacturers' new orders for consumer goods and materials, and vendor performance -- which measures the level of business activity by gauging how slowly companies receive deliveries from vendors.

The indicators making negative contributions were: net business formation, building permits, contracts and orders for plant and equipment and money supply.

One indicator -- the average workweek -- was unchanged.

Sinai said that net business formation is a relatively volatile indicator and may contribute positively to the index in the next few months, and building permits should improve because the reduction in mortgage interest rates should increase demand for new homes.

In the housing report, Commerce said that sales of new one-family houses in October were at a seasonally adjusted annual rate of 652,000, below the 690,000 rate in September and unchanged from the rate in October 1984.