The economy grew much more slowly in the first quarter than previously estimated, the government reported yesterday, prompting a top administration official to call for a new global round of interest-rate cuts to stimulate growth throughout the world.

The Commerce Department said that real gross national product -- the nation's output of goods and services -- rose at a seasonally adjusted annual rate of 2.9 percent in the first quarter, instead of the 3.7 percent rate estimated earlier. The downward revision was the latest in a series of reports suggesting a long-awaited economic rebound may be delayed, economists said.

A senior administration official said that figures for the second quarter likely will show the economy continues to be weak, and said the time has come for another coordinated round of interest-rate reductions, with West Germany and Japan leading the way.

"The global economy now looks sick," the official said.

The United States joined West Germany, Japan and other leading nations in a coordinated interest-rate reduction twice recently, on March 7 and April 18, in an effort to keep currency exchange rates stable while stimulating economic growth around the world.

Federal Reserve Board Chairman Paul A. Volcker acknowledged during congressional testimony yesterday that the economy has been sluggish for the past year, but he and some of the other six Fed governors have been reluctant to reduce rates again.

"Other strong countries, with little or no inflation, with excess capacity and historically high unemployment, and with very strong external positions, should asssume more of the leadership in providing the impetus for world growth," Volcker told the House Foreign Affairs Committee.

But the senior administration official, who did not want to be named, said that West Germany and Japan should cut their rates, and the Fed should follow with a cut in its discount rate, which is its charge for loans to financial institutions.

"I don't think it would be inappropriate for . . . West Germany and Japan to lead the charge, where we have a falling currency, and they have strengthening currencies, and where their growth has been even more anemic than ours," the official said. "But if they are willing to move, then we should be willing to join them."

The Commerce Department attributed the downward revision in U.S. economic growth in the first quarter to later data showing greater deterioration in the nation's trade position.

Economists said they were surprised by the sharp revision and said it probably would take longer than previously thought to correct the nation's huge trade deficits. With the influx of imports continuing, American companies still are not able to increase sales substantially, hire more workers and increase output, economists said.

Other recent indications of weakness in the economy were reports showing higher unemployment and lower industrial production in May.

The senior official also stressed the impact of lower oil prices on the energy sector, as well as the effects of the slide in commodity prices in general.

Prices have fallen at the wholesale and consumer levels for most of the year, but are beginning to turn up again. Last month, for example, gasoline prices rose 8.6 percent.

Interest rates also have inched up after fueling a boom in housing in the past year. Starts on construction of new housing fell 7.4 percent in May.

The long decline in energy prices was expected to lead to increased consumer spending, providing a boost for the economy, but so far the result has been lost production and increasing unemployment in oil- and gas-producing states.

Few private economists are calling for a recession any time soon, but they said the quarter ending June 30 probably will prove to be weaker than the first three months of the year. "As far as we can tell, the economy has not picked up," said Lawrence Chimerine, chief economist for Chase Econometrics. "Orders for new goods still are poor, anywhere from flat to falling. Only a handful of clients tell us orders have picked up.

"With orders so weak, we question whether we'll get . . . an upturn in the third quarter, because you need orders for production to pick up."

Although consumers seem to be spending a lot, much of their money is going toward imports and "spending on stocks and bonds," Chimerine said. "It's not going into the real economy."

Cynthia Latta, senior financial economist for Data Resources Inc., said she expects economic growth for the year to be between 2.5 percent and 3 percent. The Reagan administration forecast is for 4 percent growth.

In an interview last week, Federal Reserve Board Governor Wayne Angell said he thought the economy is "on a 2 percent growth track." But he said he would be more inclined to take commodity prices, rather than the GNP figure, as the key indicator of the need for changing monetary policy.

The Commerce Department also reported yesterday that corporate after-tax profits fell 6.6 percent last month, the steepest decline since the first quarter of 1982, during the last recession. Profits declined for manufacturers, petroleum and nonelectrical-machinery businesses. However, Commerce said that the petroleum profits "reflected in part a large payment made by a petroleum company to the U.S. Department of Energy under a federal court ruling."