The Commerce Department estimated yesterday that the economy grew at a 3.2 percent annual rate in the first quarter after the 0.7 percent rise in the final three months of 1985, prompting the Reagan administration to boast that its forecasts for a healthy expansion were coming true.

"All the recent signs of an economy gathering steam began to be realized this morning" with the Commerce report, White House spokesman Larry Speakes said.

The department's estimate of the growth in the nation's gross national product, or GNP, was a preliminary report subject to revision as later and more reliable information about the first quarter becomes available.

Several private economists, after a close look at some of the detailed figures, said the report overstates the economy's underlying rate of growth. Industrial production, for instance, now has fallen for two months in a row, and was only 0.3 percent higher in the first quarter than it was in the fourth quarter.

Both the optimists and the pessimists said the nation's output of goods and services is likely to rise at a slower pace this quarter.

With slowing auto sales and production, sharp investment cutbacks in the oil industry and a decline in federal spending because of the effects of the Gramm-Rudman-Hollings budget deficit reduction law, some analysts now think the current quarter will be very weak.

"Either the 3.2 percent figure will be revised downward or else we could end up with a zero or a negative number in the second quarter," said economist Lawrence Chimerine of Chase Econometrics. "I don't think the underlying economy grew at a 3 percent rate in the first quarter."

Economist Allen Sinai of Shearson Lehman Brothers said the Commerce report was a positive sign. "I think the economy is perking up, showing signs of responding to lower inflation, lower interest rates and a lower dollar," he said.

Speakes said that "today's good news is made even better when you consider the fact that the rebound in GNP growth was accompanied by decreasing inflation.

"The GNP price index increased [at] only [a] 2.2 percent [rate] in the first quarter compared with the fourth quarter's 3.9 percent rise," he continued, adding, "The reduction in inflation was widespread."

Sinai said the report showed strength in housing and consumer spending and in trade, with an increase in U.S. exports. "In trade, it could mean that we have turned the corner, but we can't be sure yet," he said.

Much of the improved first-quarter growth came in stronger consumer spending, which rose at a 4.3 percent pace. Most of that gain was due to a surge in purchases of non-durable goods such as food, clothing and gasoline, the department said.

Sinai said the unusually strong increase in spending for nondurables was probably the result in part of the impact of falling gasoline and home heating oil prices, which have left consumers with more to spend on other goods but not enough to go out and buy, say, a new car.

Spending for durable goods, including autos, fell at a 1.3 percent rate in the quarter.

Because of a big swing in government purchases of surplus farm commodities, figures for government purchases fell sharply while farm inventories increased substantially. The opposite had occurred in the fourth quarter.

With the drop in government spending, final sales -- the change in GNP not counting the change in inventories -- fell slightly.

Chase's Chimerine pointed to that decline, and a similar drop in final sales supplied by domestic -- as opposed to foreign -- producers as an indication that the economy is not doing as well as the overall 3.2 percent figure suggests.

He said another indication is the significant decline in business investment for new plants and equipment. Such spending fell at a 13.6 percent rate after rising at an 11.3 percent rate in the fourth quarter. A large part of the quarter's decline was concentrated in the oil industry, where drilling activity has fallen by one-third since December as a result of the plunge in oil prices.

Administration officials said the first-quarter report made it likely that its official forecast of 4 percent GNP growth between the fourth quarter of last year and the fourth quarter of 1986 would be realized.

Many private forecasters expect somewhat slower growth for the year as a whole, but just about everyone is forecasting a stronger second half as a result of lower interest rates and a declining trade deficit.

However, both Sinai and Chimerine noted that some parts of the economy are in serious difficulty, such as the oil and farm sectors. In the short run, neither expects significant gains in the industrial sector. The auto industry must work off some unwanted inventories, and production of business equipment and structures likely will be weak, too, as a consequence of flat or declining business investment.