The economy is expanding at a 7 percent annual rate this quarter, down from the second quarter's very strong 9.7 percent spurt, the Commerce Department reported yesterday.

The 7 percent rate of increase in the gross national product, adjusted for inflation, is about in line with the expectations of most forecasters, and is an indication that the economic recovery that began last December will continue for the remainder of this year and possibly for much longer.

Inflation, as measured by the GNP implicit price deflator, is running at a 3.2 percent rate this quarter, virtually the same as the 3.3 percent rate for the second quarter, the department said.

Treasury Secretary Donald T. Regan called the report "one more signal that this recovery is on track. We want solid and steady economic expansion and we are getting it."

A pleased Council of Economic Advisers Chairman Martin S. Feldstein said the numbers "are very good," adding that he expects real growth in the fourth quarter to be close to the 6.4 percent average for the first three quarters.

The 7 percent GNP figure--the department's so-called flash estimate--is based on partial and preliminary numbers, since the June-September quarter is not yet over. This was the first time that these figures have been released officially, though they have regularly been leaked in the past.

For that reason, the Commerce report warned that the figures "may be subject to larger revisions" than those in the regular GNP estimates. "Nevertheless," it added, "the flash estimates included in this release are expected to be generally reliable in indicating the direction of change in economic activity and whether the change is large or small."

In its second revision of the second-quarter numbers, Commerce raised its estimate of real GNP from a 9.2 percent rate of increase to 9.7 percent. Originally, the figure was estimated at 8.7 percent. In the first three months of the year, real GNP rose at a 2.6 percent rate.

As the second quarter figures for real output have risen, those for inflation have dropped. Estimates for the implicit deflator have gone down from 4.5 percent, to 3.5 percent, and now to 3.3 percent.

Current-dollar GNP--that is, with no adjustment for inflation--is rising at a 10.5 percent rate this quarter to a seasonally adjusted annual rate of $3,354.6 billion. The same measure increased at a 13.3 percent rate in the second quarter.

The estimate for second-quarter corporate profits, meanwhile, was revised upward. Profits from current production increased $36.4 billion to a seasonally adjusted annual rate of $218.2 billion. That is $3.5 billion above the preliminary estimate made a month ago and nearly double the first quarter's $19.9 billion increase, the department said.

Jerry Jasinowski, chief economist for the National Association of Manufacturers, said he expects the final third-quarter figures to show a stronger increase in economic activity than indicated by the flash estimate.

"There is no indication that this recovery is significantly slowing down in the third quarter," Jasinowski declared. "While the 7 percent flash estimate is itself high, it appears that the final report for the third quarter will show even faster growth, in the area of 8 percent, as retail and auto sales pick up in September.

"There is a lot of steam in the recovery for the rest of 1983," he continued. "With inventories at historically low levels, we can expect a general rebuilding of stocks in the third and fourth quarters. Healthy consumer demand and a modest pickup in efficiency-related capital spending will reinforce this trend."

However, some other forecasters think the final number for the current quarter could turn out to be lower, rather than higher, than 7 percent, particularly if consumer spending remains as weak as it was in July and August. CEA's Feldstein acknowledges that his forecast for the fourth quarter could turn out to be high if consumer spending does not get back on an upward track.

But even the more pessimistic economists generally agree that business efforts to rebuild depleted inventories will keep new orders for factory goods flowing and keep GNP rising through year's end. The fourth-quarter increase could well be no more than 4 percent or so, they say.