The economy grew at an annual rate of 6.4 per cent in the first three months of the year, substantially faster than the preliminary 5.2 per cent rate the Commerce Department reported in April.

The strong first quarter growth, which came despite the severe weather and fuel shortages of January and early February, strengthens President Carter's case that the economy is recovering nicely and does not need the boost a $50-a person tax rebate would have provided.

The President withdrew his rebate proposal in early April, to the dismay of many legislators.

The Commerce Department yesterday said it revised upward its estimates of so-called real gross national product (GNP) mainly because businessman added many more goods to their inventories than agency economists estimated they would when they prepared their preliminary GNP report.

The gross national product is the total of goods and services prodcued by American citizens. It is far from a perfect measure of a society's well-being, but it is the broadest measure economists have of how well the nation is producing goods and services.

Economists say that as a rule of thumb, a growth rate of 4 per cent must be sustained merely to keep pace with the number of persons joining the labor force. If the unemployment rate is to be reduced, economic growth must be faster than 4 per cent.

The unemployment rate was 7.3 per cent in January and rose to 7.5 per cent in February because of the weather. It fell back to 7.3 per cent in March in hit a 29-month low of 7 per cent in April, a level of the administration said it hoped to reach by the end of the year.

But Alice Rivlin, director of the Congressional Budget office, said yesterday that the unemployment rate is probably as low as it will get for th rest of the year and warned citizens not to be "surprised" if it rises a little in coming months.

Charles L. Schultze, chairman of the President's Council of Economic Advisers, said Wednesday night in a New York speech that he thought the unemployment rate would fall to between 6.6 per cent and 6.8 per cent by the end of the year.

Rivlin, speaking to a luncheon meeting of the Washington Press Club, said that after strong growth in the first and second quarters of this year, the expansion of the economy will slow to about 4 per cent during the final six months of the year.

She said that many of the factors which are causing quick growth now are "temporary."

Rivlin noted that consumers are spending a high percentage of their incomes and that the savings rate is low. She said the savings rate is likely to "come back up" later this year. She said that the inventory rebuilding businessmen have engaged in over the past few months cannot go on forever. Booms in automobile sales and residential construction also appear to be leveling off.

However, she said, business investment in plant and equipment, which has been unusually low during the current economic recovery, "seems to be coming back," and may provide some strength in the later part of the year.

Courtenay Slater, chief economist for the Commerce Department, said the strong upward revision in inventories may mean that some of the restocking economists thought would not happen until the second quarter is happened during the first three months of the year.

Nevertheless, she said, economic growth will remain strong for the first six months. She agreed with Rivlin that there will be some slowing in the final half of the year, although she declined to forecast an actual rate.

Before adjusting gross national product for inflation, which results in so-called real GNP, the economy was producing goods and services at an annual rate of $1,796 billion, compared with $1,745 billion in the final three months of 1976, a 12.2 per cent increase. In adjusted 1972 dollars, the gross national product was $1,300 billion, compared with $1,280 billion in the last quarter of 1976.

The Governement said it revised upward inventory investment, personal consumption and fixed investment, and revised downward net exports and government purchases.

The government also reported that pre-tax corporate profits rose at an annual rate of 1.4 per cent in the first quarter. After adjusting profits to account for the cost for replacing inventory, the department said profits fell at a 1.4 per cent rate to $116.2 billion.