More evidence that the economic slowdown will continue was released yesterday by the Commerce Department, which reported that the index of leading indicators fell 0.4 percent in July.

Significantly, the department also revised estimates for several earlier months, increasing the declines of the index in both the first and second quarters of the year.

Changes in the index, which has fallen 2.8 percent so far this year, often foreshadow changes in the pace of economic activity.

Courtney Slater, chief economist for the Commerce Department, said the new figures are "very consistent with the proposition that we are experiencing a mild downturn or recession.

To some extent, the index reflects the same crosscurrents now running in the economy, with some indicators rising and some falling.

In June, the most significant change in any of the 12 indicators that make up the composite index occurred in the layoff rate in manufacturing. The rate went up from 1.0 percent to 1.3 percent that month, a negative development for the economy that pulled the composite index downward.

Last month, however, the layoff rate dropped back to 1.1 percent, a positive economic development that limited the drop in the overall index to 0.4 percent.

Overall, six of the 10 indicators now available for July rose while only four declined, but some of the declines were much greater than the increases.

The biggest factor in the overall drop was a reduction in the number of companies reporting slower deliveries from suppliers. In May, 76 percent were reporting slower deliveries than in April. In June, that fell to 70 percent, and on to only 60 percent in July.

Other significant declines occurred in new orders for consumer goods and materials produced by manufacturers and in new contracts and orders for business plants and equipment -- both after adjustment for inflation -- and in building permits.

In addition to the layoff rate, other indicators that rose were the length of the average work week in manufacturing, the change in sensitive prices, stock prices, the change in total liquid assets, and the money supply adjusted for inflation.

Data on the change in inventories on hand and on order and on net business formation are not yet available for July.

Revisions in earlier estimates increased the reported decline for the first quarter of 1979 from 0.2 percent to 0.4 percent, and the second quarter drop from 1.7 percent to 2.0 percent, the department said.

The index has now declined in four months during 1979 and stayed unchanged in one. The level for July is 0.5 percent below the average for the second quarter.