The nation's economy fell further during the April-to-June quarter than was first thought, declining at an annual rate of 2.4 percent after racing ahead at a rate of 8.6 percent in the first quarter, the government reported yesterday.

The drop in the inflation-adjusted gross national product had been estimated at 1.9 percent in the Commerce Department's original report one month ago.

The department's new report said corporate profits also dropped sharply in the second quarter as the overall economy weakened.

A number of economists are predicting that inflation-adjusted GNP also will be down in the current July-to-September quarter, thus fulfilling one commonly accepted definition of an economic recession -- two consecutive quarters of negative GNP.

Murray Weidenbaum, chairman of President Reagan's Council of Economic Advisers, said recently that the nation may indeed be in its second recession in two years.

But neither he nor any private economist of note is forecasting a severe downturn this year. Most of them describe the economy as sluggish or soft rather than falling apart.

Before-tax profits fell 12 1/2 percent to a seasonally adjusted annual rate of $224.9 billion, and after-tax profits dropped 11.3 percent to a rate of $150.1 billion in the second quarter. Both rose 3 percent in the January-to-March period, the report said.

Corporate profits from current production -- a category that does not include inventory profits -- declined 7.9 percent to an annual rate of $187 billion in the second quarter after rising 10.7 percent in the first three months of the year.

Commerce Secretary Malcolm Baldrige promised that profits will improve "as the economy's growth resumes in 1982." He blamed the second-quarter decline on unsold inventories not appreciating as much in value because of lowered inflation, a fact which translated into good news for the consumer.

Yesterday's report also showed that inflation -- as measured by the broadly based GNP price deflator -- rose at an annual rate of 6.6 percent in the second quarter.