The nation's total output of goods and services climbed at an annual rate of 1.5 percent in the third quarter, after a revised 2.1 percent growth rate in the second quarter of the year, Commerce Department officials said yesterday.

Although two positive quarters normally are associated with a recovery in the economy, many private analysts believe that the United States still is mired in recession. The White House described yesterday's news as "a positive and encouraging sign," and Treasury Secretary Donald T. Regan said in New York that "we are at the start of the recovery phase."

But the White House also said that the gains in the gross national product "must be viewed cautiously." Recent monthly data for August suggest that the economy remained very weak this summer. Many economists believe that there have been no real signs of recovery, despite the July 1 income tax cut and recent sharp declines in interest rates. Unemployment is widely expected to rise still further from the 9.8 percent post-World War II high reached in July and August.

"We would say that the economy is doing no better than going sideways right now," Donald Straszheim of Wharton Econometrics in Philadelphia said yesterday, adding, "Whether it's zero or one percent , it's not any good." Straszheim also said that if the GNP is rising in the current quarter as the Commerce Department's "flash" estimate suggests, then much of this increase may be attributable to a build-up in unwanted inventories in the auto industry.

Part of the reason for an upward revision in the second-quarter GNP number, which last was estimated at 1.3 percent, is that business inventories were higher than thought previously. Real GNP, after accounting for inflation, was revised upward by $3.1 billion in 1972 dollars. Of this, an extra $1.2 billion came from higher personal consumption, $900 million from inventory investment, $600 million from government purchases and $400 million from fixed investment.

Inflation, as measured by the ENTER AREA 13GNP deflator, ran at 4.6 percent in the second quarter.

The Commerce Department also revised upward its estimate of corporate profits in the second quarter of this year. After-tax profits rose at a seasonally adjusted annual rate of 1.1 percent in the April-to-June quarter, the Commerce Department release said yesterday. Earlier, the department had estimated that profits declined at a 0.8 percent rate from the first quarter of the year. Before-tax profits were still down ENTER AREA 14from the first quarter, yesterday's report said.

Cutbacks in federal spending are being felt in the economy. Government spending on goods and services -- which excludes transfer payments to individuals who then spend their benefits themselves -- dropped at an annual rate of $7.7 billion to $32.1 billion, in 1972 dollars, during the second quarter of this year. Increased military spending partially offset the decline, rising from $74.5 billion to $78.2 billion in 1972 dollars.