Signs of a fast-deepening recession continued to mount yesterday as the government reported a record decline in construction spending and automakers announced another 40,000 new layoffs.

In the latest in a series of glum statistics, the Commerce Department reported construction expenditures plunged 5.8 percent in March, the steepest drop on record. The slide followed a 2.8 percent dip in February.

Separately, General Motors Corporation, the Ford Motor Company and American Motors Corporation announced temporary layoffs bringing the number of our-of-work autoworkers to 263,000.

The furloughs, designed to help pare excess inventories of large and medium-sized autos, are expected to last from one to three weeks. The cutbacks affect plants in several cities throughtout the nation.

The developments came as several more of the nation's largest banks followed Chase Manhattan Bank in reducing their prime lending rates to 18 1/2 percent, from 19 percent, in recognition of the worsening recession.

Citibank announced it also was lowering interest rates for residential mortgages and cooperative apartments by 1 percent, to 16 1/2 percent and 17 1/2 percent respectively.

Meanwhile, two of the nation's most prominent economists predicted the recession will prove to be decidely worse than the administration has forecast -- far from the president's assurance that it will be "short and mild."

Alan Greenspan, former president Ford's chief economic adviser, said the downturn will be "a horrible one" that easliy could rival the 1974-75 recession, which itself ws the deepest in 38 years.

And Barry P. Bosworth, former director of Carter's Council on Wage and Price Stability, warned the economy is deteriorating "in a very steady and extreme fashion." He predicted the slump would last into 1981.

Greenspan also expressed concern over the rapidity of the downturn. "I got the impression that somebody pulled the plug on the American economy" in March, he said, "and it is dropping at a much faster pace" than anyone thought.

President Carter told a group of accounting industry spokesmen yesterday he believes the economy has "turned the corner" on the inflation issue, and predicted the inflation rate "will drop significantly during the summer."

Although the president offered no new forecast on unemployment, his chief inflation adviser, Alfred E. Kahn, predicted on Wednesday the jobless rate could soar as high as 8 percent -- above the president's 7.4 percent prediction.

The Commerce Department also reported yesterday the United States' trade deficit, computed on the old "free-alongside-ship" basis, narrowed sharply in March to $2.07 billion, from $4.41 billion in February.

The government announced earlier this week using a new computation required by law, the trade of deficit for March was $3.16 billion, from $5.57 billion in February. By law, officials must delay publication of the f.a.s figures.

In separate action yesterday, the Council on Wage and Price Stability recommended Congress scrap or delay requirements that federal buildings and housing projects meet certain energy conservation standards by 1982.

The agency said over the past five years the energy situation "has changed considerably" and the previous standards no longer are workable.