A government index designed to foretell the economic future fell in July for the first time in six months, another sign that economic activity may slacken in the months ahead.

The administration has already forecast some such slackening. In addition, however, the Federal Reserve Board - so far with White House approval - has recently been busily driving up interest rates to discourage borrowing and cool off the economy, as a way of fighting inflation and propping up the declining dollar.

White House economists said yesterday that they still support what the Fed is doing. The 0.7 per cent decline in the Commerce Department's index of leading economic indicators was not cause for concern and was within expectations, they assured reporters.

But officials conceded privately that they may have to reconsider their stand on rising interest rates if the economy falters more than expected and higher rates threaten to choke off growth in the coming months.

In another development, the Council on Wage and Price Stability, concerned about the escalating costs of building a home, announced an investigation of rising prices of building materials such as gypsum, cement, asphalt roofing and lumber products (Details on Page E1).

While most analysts say the Fed's actions to raise interest rates - they have risen 1 1/4 percent since the spring - have not hurt the economy, the administration is working on a second phase of its voluntary program to reduce wage and price increases.

Yesterday, White House spokesman Jody Powell said there is nothing to Wall Street rumors that the president was about to make a statement on wage and price guidelines.

Powell told reporters that the president still is opposed to any form of wage and price controls, and denied another Wall Street rumor that Carter soon will impose a fee on oil imports.

The last time the Commerce Department's index of leading economic indicators fell was in January, when heavy snows, cold weather and a coal strike combined to depress the economy. The economy rebounded from its winter doldrums, growing sharply in the spring and then settling into a growth rate averaging between 3.5 percent and 4 percent.

Analysts say the economy must grow about that fast to keep the umemployment rate from rising. Unemployment has been struck around 6 percent for most of the year.

The decline in the indicators is another sign of the slackening economic pace. Wednesday the Commerce Department reported a sharp decline in new orders from factories, and the Conference Board reported that companies are planning to spend less on new plant and equipment now than they were several months ago.

Feliks Tamm, a Commerce Department analyst, cautioned that the 0.5 percent rise in the leading indicators in June and the 0.7 percent decline in July were both exaggerated by the June vote in California to slash property taxes.

That vote spawned a rash of applications for building permits in California. That made the June increase bigger than it should have been and the decline in building permits to a more normal level showed up a serious decline in July.

Tamm said that, after adjusting for the California situation, the index rose only 0.1 percent in June and fell 0.4 percent in July.

Five of the 10 statistics used to compute the index performed adversely, three remained unchanged and two rose.

The department said there was a significant decline in the number of companies reporting slow deliveries, an indication that factories were less backed-up with orders than before.

Stock prices, the money supply adjusted for inflation, building permits and new orders for consumer goods also fell.

The length of the average work week was unchanged, as was the lay-off rate.

Prices of crude materials rose, supposedly an indication of increasing activity, and contracts and orders for plant and equipment orders, adjusted for inflation, also rose.