A new round of government economic statistics released yesterday shows the recession may be coming to an end but the recovery still is likely to be sluggish.

The Commerce Department reported that retail sales surged a respectable 1.5 percent in August following a revised 3.1 percent increase in July. The latest rise was the third consecutive monthly increase.

At the same time, however, the agency disclosed that American business again has trimmed its capital spending plans for this year, suggesting the coming recovery may not be as strong as had been hoped.

In its latest quarterly survey of business spending plans, the department reported capital outlays are now likely to rise by only 8.7 percent over 1979 levels -- actually a slight decline, after inflation is taken into account.

In similar surveys conducted in June and March, businesses estimated their capital spending would increase by 9.9 percent and 11.1 percent, respectively. Strong capital outlays are considered vital to the recovery.

In other economic reports yesterday:

The Federal Reserve Board announced that the amount of installment debt consumers have outstanding shrank by a moderate 2.5 percent in July, in its fourth such decline in a row. However, new credit extended rose 18.4 percent.

The Labor Department disclosed that initial claims for state unemployment insurance -- often a harbinger of changes in the national jobless rate -- rose by 13,000 during the week ended Aug. 30, reversing a decline in previous weeks.

The Federal Trade Commission reported that after-tax profits of manufacturers slid to 4.8 percent of sales in the second quarter, down from 5.3 percent in the previous period and 6.1 percent a year earlier.

The new figures on retail sales were seized upon by the Carter administration as further evidence that the recession may finally be nearing an end.

Commerce Secretary Philip M. Klutznick issued a statement yesterday saying they "reinforce the possibility that the low-point . . . has been reached and that the recovery may be beginning more promptly than had been expected."

He said the recession may prove to be "the shortest since World War II."

Klutznick traditionally has not commented publicly on individual retail sales reports.

The increase in retail sales brought total consumer buying to a seasonally adjusted $79.53 billion, up from $78.39 billion in July. In a preliminary estimate previously, the department had reported the July rise as 2 percent.

The report showed a respectable 2.4 percent rise in sales of durable goods, following a hefty 8.3 percent jump in July. Auto sales climbed by 2.8 percent after surging 12.8 percent in July.

The department reported that sales of nondurables rose 1 percent in August, following an 0.9 percent increase in July. Overall, retail sales were up 6.2 percent from their level of August 1979.

The survey on capital spending showed overall outlays for new plant and equipment now likely to reach $192.5 billion in 1980. In 1979, total business investment was $177.1 billion, or 15.1 percent over that of 1978.

Yesterday's report showed the downward revisions from earlier surveys concentrated primarily in durable goods manufacturing industries, such as autos and steel, and in transportation and communications firms.

In its figures on individual installment debt, the Fed estimated the July decline in consumer credit at $609 million, compared with a $3.46 billion plunge in June.

The central bank said extensions of new credit for auto purchases rose to a seasonally adjusted $6.61 billion in July, up from $4.77 billion the previous month, while overall auto credit outstanding fell $93 million in July.

Revolving credit outstanding, including credit card debt and checking account credit at commercial banks, rose $14 million in July after declining $748 million in June.