Paced by sharp increases in federal government spending and new car purchases by consumers, the American economy grew at a 3.3 percent annual rate in the third quarter, the best gain so far this year, the Commerce Department reported yesterday.

However, the increase still fell short of Reagan administration predictions that the gross national product, adjusted for inflation, would climb at a 5 percent rate in the second half of this year, following the first half's anemic 1.1 percent pace.

The preliminary 3.3 percent figure for the third quarter was higher than the department's 2.8 percent "flash" estimate computed before the quarter ended.

Meanwhile, all three GNP price measures showed inflation running at about a 3 percent rate last quarter, down from about 4 percent in the first six months of the year.

Separately, Commerce also reported that starts of new housing units fell 9.3 percent in September, to an annual rate of 1.583 million, the lowest level in nearly a year. The number of single-family houses started also slipped below the 1 million-unit level for the first time since last October. Details on Page E1.

At the White House, spokesman Larry Speakes issued a statement declaring, "The economy is clearly performing well, with most elements running comfortably ahead of our 'flash' estimates. With inventories now at a very low level and consumer demand very strong, we expect a sharp increase in production and continued acceleration of growth in GNP."

While some private economists also expect GNP growth to continue to accelerate, others believe that consumer spending, the economy's most solid prop all year, will soon weaken. Some forecasters, such as those at Data Resources Inc., expect consumer spending, which accounts for nearly two-thirds of GNP, to decline this quarter.

Lyle Gramley, who left the Federal Reserve Board this summer to become chief economist for the Mortgage Bankers Association, said the GNP numbers "do confirm a moderate improvement in the economic expansion, but I would emphasize 'moderate.' It is hard to get too enthusiastic over what you are looking at."

Gramley said that other recent economic statistics, such as those for employment and industrial production in September, "do not imply any substantial improvement in economic activity . . . . This is not a robust economy." Rather, he said, the latest evidence "is consistent with something close to 3 percent growth in the fourth quarter."

And one Reagan administration economist noted, "We don't have any real signs of sustained improvement yet." The official said a pickup in growth this quarter sharp enough to reach the predicted 5 percent rate for the second half of the year has a "low probability" of occurring, but is still possible.

With consumers taking advantage of reduced interest-rate financing offered by the automotive industry to help sell the remainder of its 1985 models, their outlays for durable goods shot up at a 20.5 percent rate in the third quarter, Commerce estimated. The latest car sales figures, for the first 10 days of October, show a large drop compared to September.

Spending for nondurable goods, such as clothing and food, rose at only a 0.7 percent rate, the smallest increase since the first quarter of 1982. Purchases of services went up at a 3.4 percent rate, the lowest since the first three months of 1984.

"The American consumer is overextended," said Stephen S. Roach, an economist at Morgan Stanley & Co. During the past four quarters, real disposable income has gone up roughly 1 1/2 percent, about one-fourth as fast as it did in the first seven quarters after the end of the 1981-82 recession. Historically, such a slowing of income gains has been followed by a retrenchment in spending, he said.

In the short run, less strength in consumer spending may be offset to some extent by continued increases in defense spending, which also rose at about a 20 percent rate in the third quarter.

Nondefense government spending increased at an even faster rate as farmers, faced with a huge fall harvest and very low market prices, put a significant share of the crop "under loan" -- that is, it was used as collateral for a loan from the Commodity Credit Corp. Such a loan shows up as a federal purchase, to be offset in the future as a reduction in spending when the loan is paid off or the actual commodities are sold. Another large increase in federal spending for this purpose is expected this quarter.

At the same time, business inventories are likely to start to grow again, increasing the demand for goods, analysts said. In the third quarter, businesses reduced their stocks at an $8 billion annual rate, an enormous swing -- even in a $3.9 trillion economy -- from the same quarter in 1984 when they added to their inventories at a $71.8 billion rate.

This big shift from inventory building to inventory liquidation is a major factor in the slower growth for the economy during the past year.

However, gains in business capital spending have also slowed down, declining at a 4.7 percent rate in the third quarter. Such outlays moved erratically in the first half, falling at a 1.6 percent rate in the first quarter and bouncing back smartly to a 14.5 percent rate of increase in the second.

One reason for a slowdown in investment is the substantial level of unused productive capacity at the nation's factories, mines and utilities. The Federal Reserve Board said yesterday that the use of available capacity dropped from 80.3 percent in August to 80 percent last month. A year earlier, the figure was 81.7 percent, and even that was well below levels preferred by business.

Meanwhile, the nation's international trade balance, the worsening of which has been another significant factor holding back production of domestic goods, hardly changed in the third quarter. The nominal value of imports actually declined, but so did their prices, so that the volume of real imports rose slightly, as did the volume of real exports.

What the GNP figure will show for the current quarter is uncertain. Some analysts, such as Morgan Stanley's Roach and those at DRI, think it will rise at about a 2 percent rate despite a small decline in personal consumption spending.