The government's index of leading indicators -- aguide to the future course of the economy -- climbed by 1.3 percent in July, the fourth consecutive monthly increase after 11 months of decline, the government reported yesterday.

White House spokesman Larry Speakes called the increase "moderately encouraging," while Commerce Secretary Malcolm Baldrige said "the significant pickup" is "encouraging evidence that economic recovery is about to get under way."

Most economists believe that there will be a recovery in the final months of this year, although it is widely expected to be weaker than the average postwar upturn. Recent declines in interest rates likely will help the recovery.

Another government report yesterday said that factory orders rose by 2 percent in July. The Commerce Department release said that the July increase was the largest in one month since December 1980. The July increase came after a 0.2 percent climb in June that originally was estimated as a 0.3 percent decline.

Durable goods orders, which have been hard hit during the recession, rose by 4 percent in July compared with a decline of 1.5 percent in the previous month, the report said.

Meanwhile in Detroit, General Motors Corp. announced yesterday that it will reduce or freeze base prices on more than half of its 1983 passenger-car models, Associated Press reported.

But GM also will increase prices by between $357 and $686 on 60 full-size cars, luxury models, some mid-size cars, and the sporty Chevrolet Camaros and Pontiac Firebirds, which have been selling well this year.

GM will cut $250 from the prices of its mid-size A cars -- the Chevrolet Celebrity, Pontiac 6000, Oldsmobile Ciera and Buick Century -- and up to $500 from comparably equipped subcompact J cars -- the Chevrolet Cavalier, Pontiac 2000, Oldsmobile Firenza and Buick Skyhawk.

The price of the Cadillac Cimarron will remain the same, but $400 worth of equipment will be added, the statement said.

[Prices also will be frozen for the subcompact Chevrolet Chevette and Pontiac 1000 and the compact X cars -- the Chevrolet Citation, Pontiac Phoenix, Oldsmobile Omega and Buick Skylark.]

Yesterday's economic news suggests that "we will have a meaningful recovery in place in the fourth quarter" of the year, Allen Sinai of Data Resources Inc. said. However, he added that this recovery does not seem to have begun yet. "What's in process now is still a bottoming out," with weak auto sales and depressed prospects for business investment, he said.

In July, seven of the 10 available indicators that make up the leading index contributed to the gain. The biggest of these were increases in building permits for future construction and rising prices for raw materials. The latter is often an early reflection of an increase in industrial demand, although it also contributes to inflation.

Other factors helping to push the index up in July were the average work week, initial claims for unemployment insurance, manufacturers' new orders for consumer goods and materials in 1972 dollars, contracts and orders for plant and equipment in 1972 dollars, and changes in the money supply after adjusting for inflation.

Among the negative indicators in July was the stock market. However, stock prices soared in August in a week of frenzied activity so that this will help to boost the August index. Changes in total liquid assets also exerted a downward influence on the index. This "means that business continues to face a cash squeeze," commented Jerry J. Jasinowski, chief econmist of the National Association of Manufacturers. However, Jasinowski also declared himself "confident that the economic picture will continue to brighten during the next couple of months, although slowly."

President Reagan originally predicted that the economy would begin to recover from recession this spring. There was an upturn in the nation's gross national product in the second quarter of the year, although this was largely for technical reasons, analysts said. Most forecasters expect the third quarter to be flat, despite the 10 percent cut in income taxes that became effective at the beginning of July.

The July increase in leading indicators followed rises of 1.4 percent in April, 0.7 percent in May, and 0.3 percent in June. The June index originally was estimated to be flat.

The recession, which has pushed unemployment to its highest level since World War II, was characterized by extremely high interest rates, which persisted much longer than most experts predicted. These have come down sharply in the last few weeks, but several analysts expect their impact on business spending plans to linger for months. Capital spending is likely to be one of the weakest sectors of the economy for some time to come.

Baldrige agreed that "key coincident indicators, such as payroll employment, industrial production, and real GNP are unlikely to show much change for the third quarter." However, he said lower interest rates are helping to pave the way for "solid economic improvement" while the August stock market rally signalled "investors' relief over passage of the tax bill and confidence in renewed economic growth."