The nation's economy grew at a surprisingly sluggish 1.3 percent annual rate in the first quarter of the year as a rising trade deficit offset gains elsewhere, the Commerce Department reported yesterday.

The inflation-adjusted increase in the gross national product was well below expectations and the smallest quarterly gain since the recession ended in late 1982. The GNP report raised new questions about the pace of the economic expansion for the remainder of this year.

White House Chief of Staff Donald T. Regan, responding to the report, said "at this moment, the economy is not healthy." According to the Knight-Ridder news service, Regan told a group of news executives that the figures could presage a recession unless Congress adopts President Reagan's plan for reducing federal budget deficits.

The 1.3 percent increase in GNP followed increases at a 4.3 percent rate in the fourth quarter and 1.6 percent in the third quarter of 1984. Last month, before the quarter had ended, the Commerce Department had predicted the increase would be 2.1 percent.

The GNP report reflects the fundamental deterioration in the nation's balance of trade. In the past, when exports generally were larger than imports, the GNP was a measure of the nation's total demand for goods and services. With imports now larger than exports, total demand is larger than the GNP by the amount that imports exceed exports.

Total demand, figured this way, rose at a healthy 4.4 percent rate in the first quarter, but most of that increase was not translated into domestic production because of the imports. For instance, the first quarter deterioration of the trade balance, with exports declining somewhat and imports going up strongly, was greater than the entire increase in consumer spending during the quarter.

Economist Alan Greenspan of Townsend-Greenspan & Co. said the 1.3 percent figure may be understating the actual rate of real growth but that even so "it is still a low figure." The issue, he said, is "not that there is an underlying erosion of growth" but that imports are meeting an ever increasing share of domestic demand.

The value of the U.S. dollar on foreign exchange markets has been dropping swiftly since March, Greenspan noted. But it will still take a substantial length of time and additional declines before a cheaper dollar will have much impact on the trade balance, he said.

The sluggish GNP performance will also have an adverse impact on the federal budget deficit. Continued slow growth would swell the federal budget deficit, already estimated by the administration at $213 billion for fiscal 1985. If the first quarter's shortfall in expected economic growth were to be repeated in succeeding quarters, the deficit probably would be increased by $13 billion to $15 billion this year and by more in fiscal 1986, analysts said yesterday.

Inflation accelerated somewhat in the first quarter, rising at a 5.3 percent rate, compared with 2.8 percent in the fourth quarter as measured by the GNP implicit price deflator. However, that price measure is affected by changes in the mix of goods and services actually bought, and much of the increase was because of a rise in energy purchases.

By another measure, the GNP fixed-weighted price index, the inflation rate increased to 4.4 percent from 3.6 percent the previous quarter. About half that rise was because of a federal pay increase in January, the Commerce Department said.

Over the last nine months, the gross national product has grown at a 2.4 percent rate in real or inflation-adjusted terms. Earlier this week, the Reagan administration said it expects real GNP to rise 3.9 percent during the four quarters of 1985.

In making that forecast, the administration incorporated the so-called flash estimate of first quarter GNP that showed it rising at a 2.1 percent rate, which Commerce calculated on the basis of partial data before the quarter ended. Sources said that the administration then assumed that real GNP would rise at a 5.6 percent rate this quarter before settling back to a 4 percent rate in the second half of the year. It was on the basis of this forecast that the administration projected a $213 billion budget deficit for fiscal 1985.

In current dollars, as opposed to an inflation-adjusted basis, GNP rose 6.7 percent to a seasonally adjusted annual rate of $3,819.9 billion, up from $3,758.7 billion in fourth quarter.

Meanwhile, business investment in new plants and equipment also increased at a much slower rate, 3.5 percent, than it did last year. Such investment, which rose almost 20 percent in 1984, has been going up more slowly with each successive quarter. It rose at a 13.7 percent rate in last year's third quarter and at an 8.5 percent rate in the fourth.

Residential investment fell at a 0.8 percent rate, less than in the two previous quarters but still the third decline in a row. Government purchases of goods and services were virtually unchanged from the previous quarter.

A number of forecasters are revising downward their estimates of real growth for this year, a few are calling for either recessions or extremely slow growth and rising unemployment in coming quarters. However, still others expect a sharp rebound in growth beginning this quarter.

Stephen S. Roach of Morgan Stanley & Co., one of those who has a very pessimistic outlook, said the trade balance is only one of several problems the economy faces now that the immediate post-recession recovery phase is over.

"Of greatest significance is the pronounced slowing in business capital spending -- an abrupt downshift from the record investment binge of the past two years," he told his company's clients this week.

There are also potential problems in the level of business inventories, Roach continued. "To be sure, personal consumption still looks to be in reasonably good shape, but even here, the question is: How long can the consumer go it alone."

The Morgan Stanley forecast shows virtually no increase in real output this quarter and only a 1 percent gain during the year, compared to the administration's 3.9 percent forecast.

"The expected first-half weakness is sufficient, in our judgment, to affect income, inventories and, ultimately, consumption . . . With the economy expected to be essentially stagnant for the next several quarters, labor and product markets should also show some slack. The unemployment rate is projected to rise above 8 percent late in the year, and the capacity utilization rate [for] factories should be moving down close to 77 percent [from 80.8 percent in February and March]".

Most forecasters are more optimistic than that, and as one analyst put it, "The Fed would never let that happen." Fed Chairman Paul A. Volcker has recently expressed serious concern that some sectors of the economy, principally manufacturing, mining and agriculture, are not sharing in the recovery.

Commerce Undersecretary for Economic Affairs Sidney Jones said that he expects that growth in the current quarter will be higher than in the first quarter. Jones said that when employment is rising by 350,000 to 400,000 jobs a month, as it did in March, there will be strong personal income gains and continued growth.

But Jones also noted that personal consumption was the only strong area in the first quarter, and that imports are satisfying that added spending. "That's the bottom line of the GNP report," he said.