Industrial production continued to drop sharply last month, the Federal Reserve reported yesterday, but Carter administration and private economists said there is evidence the economy's slide into recession has slowed.

Output of the nation's factories, mines and utilities fell 2.4 percent in June, the Federal Reserve said. There was a similar 2.4 percent decline in May and a 2.2 percent drop in April.

Charles Schultze, chairman of the Council of Economic Advisers, said the June decline in production indicated businesses are reducing their inventories. Consumer purchases of many goods, including autos, picked up a bit last month, and with production continuing downward, those sales must have been made from stocks on hand, he explained.

With the drop in production, Schultze said the gross national product, after adjustment for inflation, probably fell at an annual rate of between 8 percent and 9 percent in the second quarter "and conceivably may edge above that." Administration officials have previously talked of an 8 percent or 8.5 percent rate of decline for the quarter just ended.

Schultze believes any reduction in inventories will be small because most businesses have kept their stocks very lean by quickly cutting production whenever sales declined.

"I think this recession will slow down shortly and will turn around" and be followed by "a slow, slow recovery next year," Schultze told the Washington Women Economists Club.

The presidential adviser added, "I think all the factors point in that direction."

For one thing, they very quick response of business to keep inventories in line means more of the recession's decline was packed into the second quarter, in which the economy may have fallen faster than any other quarter since World War II. On the other hand, that same responsiveness suggests production could turn upward again as soon as it is certain sales are improving, analysts said.

Some other economic statistics due to be released today could lend support to Schultze's view the economic decline is slowing.

With the sharp decline in mortgage interest rates since April, housing sales have risen and information on new housing starts in June, which the Commerce Department will release today, may show an increase over May.

Similarly, while data on personal income, also due from Commerce today, will reflect a significant decline in employment and hours worked last month, other figures on personal outlays by individuals likely will confirm their buying increased in June, the analysts said.

Meanwhile, the industrial production figures clearly indicate the nature of the recession changed somewhat in June, Schlutze said.

Big drops in automobile and truck production was key factors in the April and May declines. Production of light trucks continued downward in June, but auto assemblies rose about 7 percent last month in the wake of better sales.

At the same time, production of business equipment fell 2.3 percent, more than twice as fast as in the previous two months. The output of durable-goods materials declined by almost 4 percent, largely reflecting further sharp decreases in production of steel and parts for equipment and consumer durables. And nondurable-goods materials production dropped 4.2 percent, as the output of textiles, paper and chemicals all fell, the report said.

Production of construction supplies went down another 4.5 percent in June, following a decline of 7.3 percent in April and 4.7 percent in May.

Schultze said he is confident the recession would end before long because both inflation and interest rates -- whose high levels helped cause such a severe recession in the first place -- have come down so swiftly from their peaks.

The Carter adviser also was critical of proposals by GOP presidential candidate Ronald Reagan for an immediate tax cut to stimulate the economy. The large cuts proposed by Reagan would not meet the long-term needs of the U.S. economy, Schultze argued.