The government's index of leading economic indicators last month increased 0.3 percent, the smallest rise since the recovery began and the latest indication that the economy's power may be losing some of its punch.

The rise in July was the 11th consecutive monthly increase, but its small size indicated to some government and private economists that the economy within the next six to nine months may be reaching a plateau of "neither boom nor bust," as two leading economists put it. However, that isn't bad news, but a normal, healthy stage for a sustainable recovery and means there is less pressure for inflation or higher interest rates next year, several economists said.

Perhaps encouraged by the outlook, the stock market posted its sharpest gain in six weeks yesterday, with the Dow Jones industrial average rising 20.12 points.

Homebuilding and consumer spending already are leveling off from furious bursts of activity earlier this year. During normal recoveries, this is followed by a pickup in business investment. However, government economists said they were slightly disturbed by a drop in business investment activity in July, which should be picking up about this time.

"July's modest rise in the leading index is an early indication that the economic rebound of the second quarter will taper to a more sustainable pace," said Commerce Secretary Malcolm Baldrige. "Almost every postwar recovery from recession has had one or two quarters of abnormally high growth," he said, stemming largely from a rebuilding of inventories.

The slowing of the economy follows high growth in the second quarter with GNP increasing at a 9.2 percent rate. Economists feared that if growth continued at that pace it would fuel inflation and lead to a further tightening of the money supply by the Federal Reserve Board. The consequence would be higher interest rates, which would blunt any further gains in economic activity.

Although a slowing of the economy was considered a good sign, Robert Ortner, Commerce Department chief economist, said the government would prefer to see gains in the index of between 0.5 percent to 1 percent per month to maintain a sustained recovery. The index increased 1.9 percent in June and 1.2 percent in May, according to revised figures.

Other economists said the July figures were not the only indications of a slowdown. Otto Eckstein and Roger Brinner, economists for Data Resources Inc., predicted that a slowdown in retail sales, orders for durable goods, housing starts and money growth "indicated a clear deceleration or plateau in activity" for the future.

"The most likely economy for the second half of 1983 and for the next two years is one characterized by neither runaway demands and prices nor renewed recession," Brinner and Eckstein said in a forecast report. Under those conditions the Fed "can succeed in tempering the recovery without killing it."

Most economists still expect rapid growth in the third quarter, but the slowdown will be noticeable by the end of the year.

However, some economists said it is difficult to foresee the economy's future course based on indicators taken during volatile summer months. Jerry Jasinowski, chief economist for the National Association of Manufacturers, said it is too early to predict a slowdown in the recovery on the basis of the July indicators.

Seven of the 11 leading indicators in the Commerce report contributed to the increase. They were average workweek, average weekly initial claims for state unemployment insurance, manufacturers' new orders for consumer goods and materials, building permits, stock prices, money supply and change in credit outstanding. The government said the change in credit, a sign of consumer confidence and willingness to spend, contributed the most to the increase.

However, Ortner said the three indicators that decreased were "somewhat disappointing." Net business formation, contracts and orders for plant and equipment and change in sensitive materials prices all decreased. Contracts and orders for plant and equipment contributed the greatest to the decline and consisted mainly of a drop in activity in the aircraft construction industry.

An accompanying index for coincident indicators, which measures what is currently occurring in the economy, rose by 1.1 percent in July following increases of 1.1 percent in June and 1.8 percent in May.

In a separate report, the Agriculture Department said August farm prices rose 4.6 percent after falling by 2.2 percent in July and June.