The index of leading indicators rose 0.3 percent in May, marking the third consecutive monthly increase and offering additional evidence that the recession has hit bottom, the Commerce Department reported yesterday.

But the modest size of the increase in the index--which is a composite of 12 separate indicators and which often moves up or down in advance of similar changes in the economy--reinforced the view of some analysts that the recovery will be slow and perhaps not sustained.

Treasury Secretary Donald T. Regan, in St. Louis to speak to a business group, said the increase was one of several "hopeful signs. We could get some bad figures later on. We're not out of the woods entirely, but it is pretty clear we are emerging from this recession," he declared.

Murray L. Weidenbaum, chairman of the Council of Economic Advisers, told reporters that recent statistics have convinced him "the economy is turning around. There is a lot of actual support for that."

However, Weidenbaum also warned that "unemployment may not have peaked. . . . It peaks after the economy turns. We will get a sustained decline only when employment is growing fast enough to absorb growth in the labor force." The June unemployment rate will be reported on Friday. It stood at 9 1/2 percent in May. Most forecasters are predicting an increase to 9.7 or 9.8 percent.

Five of the 10 leading indicators available yesterday rose in May and five fell. Sensitive crude materials prices contributed the most to the gain in the composite index, while contracts and orders for business plant and equipment declined the most, the department said.

Robert G. Dederick, designated recently as under secretary for economic affairs, said, "While less than expected, the May advance . . . is consistent with other data suggesting that the recession has bottomed out. In the immediate future, the consumer sector apparently will be the key contributor to recovery. As indicated, though, by the setback in contracts and orders for new plant and equipment, business capital spending is likely to decline further."

Forecaster Lawrence Chimerine, head of Chase Econometrics, saw the numbers as "fundamentally consistent with what we expect, namely, that the economy is now bottoming out and a modest improvement will occur in the second half of the year." But he said that the recovery will be "relatively slow."

Both Regan and Weidenbaum said they expect interest rates, whose high level is a danger to the recovery's prospects, to fall later this year. However, Weidenbaum echoed the Treasury secretary's assessment a few days ago that they will go higher before turning downward. "In the very short run, the prospect is higher interest rates. Then I hope the trend is down."

Weidenbaum disassociated himself from recent pointed criticism by Regan and the Treasury undersecretary for monetary affairs, Beryl Sprinkel, of the way in which the Federal Reserve has been executing monetary policy. The CEA is not participating in the Treasury's review of whether the Fed's independence from the executive branch of government should be curtailed in some way, he said. "The White House has ordered no such review. . . . I am not sure whether Mr. Sprinkel gives marching orders to Mrs. Sprinkel, but it doesn't extend beyond the family."

Separately, the Commerce Department reported that new orders for manufactured goods rose $2.4 billion, or 1 1/2 percent, in May to a level of $158.1 billion. Shipments, however, rose even faster, up $4.1 billion, or 2.6 percent, to $161.2 billion. As a result, order backlogs at the end of May stood at $314.8 billion, down 1 percent from April.

The book value of manufacturers' inventories decreased $2.7 billion, or 1 percent, in May to $271.5 billion. It was the fifth decline in the last six months for inventories, the department said.