The growth for the nation's economy slowed to a crawl during the first three months of this year, the government reported yesterday -- bolstering assertions by the Carter administration that the recession finally is underway.

Commerce Department figures showed the "real" gross national product -- or physical volume of goods and services produced -- grew at an annual rate of only 1.1 percent last quarter, compared to a 2 percent pace in late 1979.

At the same time, largely in recognition of the slowed economic pace, several of the nation's major banks reduced the prime lending rate for large corporate customers to 19 1/2 percent from 19 3/4 percent.

Courtenay M. Slater, the Commerce Department's chief economist, said the figures on output showed "an economy that peaked in January and then began a slide into recession." She said output would decline this quarter.

However, Treasury Secretary G. William Miller, out stumping for President Carter in advance of next week's Pennsylvania primry, predicted the downturn would be mild and short.

The Treasury cheif told a news conference after a luncheon speech in Pittsburgh that the economy would beginto recover "by the end of the year." He also forecast that inflation would fall below 10 percent by 1981.

The first-quarter slowdown reflected visible declines in several key sectors of the economy, including a sharp falloff in consumer spending, whose unexpected buoyant last year helped stave off the predicted recession.

After adjustment for inflation, spending for nondurable goods, a key indicator to many economists, declined at an 0.6 percent annual rate, following a rise at a 7 percent rate in the final three months of 1979.

Housing construction also plummeted, declining at a staggering 20.1 percent annual rate last quarter following a drop at a 4.5 percent pace in the final period of 1979. Home sales have been crimped by soaring mortgage rates.

At the same time, the figures showed inflation accelerated significantly. The GNP price index, considered the broadest measure of inflation, rose at an annual rate of 9.5 percent last quarter from an 8.4 percent in late 1979.

The inflation figures shown in the GNP price index are far below the 18.2 percent annual rate posted by the monthly consumer price index so far this year -- partly because the latter is bloated by home mortgages rates.

The department's "personal consumption deflator," a measure many economists regard as a good approximation of living costs, rose at a 12.6 percent annual rate last quarter, compared to a 9.7 percent pace in late 1979.

Slater told a news conference yesterday that despite the abrupt slide in February and March, it still appeared unlikely that the recession would be as severe as that of 1974-75, which was the worst slump in 36 years.

At the same time, however, she cautioned that the recovery -- which she predicted would come sometime later this year -- most likely would be weak. She described the current slump as apt to be "moderate."

The drop in the prime lending rate was the second this week. The initial decline, to 19 3/4 percent, from a high of 20 percent before, was taken as a sign that interest rates had peaked.

Yesterday, White House inflation fighter Alfred E. Kahn told a business group in Dallas that the drop in the prime was a sign that Carter's "intensified economic program seems to be beginning to work."

Yesterday's GNP report also showed these developments:

Real final sales, the broadcast measure of buying activity, slowed visibly during the period, rising at a 1.5 percent annual rate last quarter.

The savings rate remained low, but did not continue to slide. Savings totaled 3.4 percent of disposable income last quarter, compared to 3.5 percent the previous period.