The government's main gauge of future economic activity rose 0.4 percent in September after declining for three consecutive months, but other economic statistics issued yesterday raised warning signals.

The Commerce Department, which reported the rise in the leading indicators for September, also said it had revised the index for August to show a decline instead of the increase initially estimated. The 0.1 percent drop for August followed declines of 1.7 percent in July and 0.9 percent in June.

The department also said the nation's merchandise trade deficit widened to $12.6 billion in September, after shrinking from $14 billion in July to $9.9 billion in August. After nine months, the 1984 trade deficit totaled $96 billion, Commerce said.

And in another report, Commerce said new orders for factory goods fell 1.8 percent in September, following declines in August and July.

Taken together, the three reports painted a picture of an economy slowing abruptly from the fast pace of the beginning of the year without yet reaching a recession, economists said.

Many economists have said that three monthly declines in a row in the index of leading indicators -- which forecasts economic activity six to nine months in the future -- was a signal of a recession. However, analysts said yesterday they said a recession did not appear imminent, but that growth could slow enough to cause the unemployment rate to rise.

The White House, attempting to discourage talk of a recession, said the upturn in the leading indicators for September showed that the "expansion continues at a sustainable pace."

"The leading economic indicators show the economy is maintaining its strength and heading in the right direction," said White House spokesman Larry Speakes. "The downward trend in interest rates . . . adds to our confidence about future economic growth."

Commerce Secretary Malcolm Baldrige said that the increase in the index of leading economic indicators in September "should ease concerns that the economic expansion is coming to an end.

"There have been several occasions in the past when three consecutive declines were followed by slowdowns and not recessions," he said. "Moderate growth is what I expect for the rest of 1984 and 1985."

Baldrige said the economy should continue to grow because consumers have stepped up their spending after a pause in the summer, and business investment is still strong. He also said hefty defense production should prevent an economic downturn.

Some private economists also noted interest rates are declining, inflation is still in check and the Federal Reserve Board, after keeping a tight fist on money growth earlier this year in an effort to prevent an acceleration in inflation, has loosened its grip somewhat, which should lead to a pickup in economic activity.

However, other private economists were less sanguine.

Allen Sinai, chief economist for Shearson Lehman/American Express, said a recession cannot be ruled in or out at this point. Three months of downturn in the economic indicators "could be a false signal. It does raise a warning or a flag of a small downturn in 1985."

Roger Brinner, chief economist for Data Resources Inc., said, "1985 is likely to be a soft year." Brinner said that although spending is again rising, a lot of it is being diverted to imports, explaining the large trade deficit.

In addition, because spending on imports is strong, production at U.S. factories isn't growing as rapidly as it could, which explains the declines in new orders of some manufactured goods. In the future, import spending would result in lower incomes in the United States and consequent slower growth, Brinner said.

Six of the 11 leading indicators available for September rose. They were net business formation, change in credit outstanding, money supply, average workweek, stock prices and vendor performance, which measures the level of business activity by gauging the size of the backlog in deliveries of goods.

The declining indicators were manufacturers' new orders for consumer goods and materials, building permits, average weekly initial claims for state unemployment insurance, change in sensitive materials prices, and contracts and orders for plant and equipment.

Some measures used by economists to gauge future economic activity -- new orders for consumer goods and materials and orders for plant and equipment -- have been weak in recent months, causing concern among some economists.

In its report on orders for factory goods, Commerce said new orders for nondefense capital goods fell 1.4 percent in September, following a 4.2 percent decline in August.