Construction of new homes plunged 2.4 percent last month, surprising many economic forecasters and raising fears that the economy is headed for further stagnation instead of the rebound the Reagan administration and private forecasters had expected.

The housing report was the latest in a string of disappointing economic statistics showing that consumer spending is sluggish, business purchases are down, automobile sales are off, factory output is still below levels of a year ago and imports are gaining an increasing share of U.S. business.

Factory employment is down by 220,000 since the beginning of the year, incomes are growing slowly and the unemployment rate has been stagnant at a historically high level for the past six months.

Although few economists expect a recession, upbeat predictions of a strong economic comeback are disappearing. Of all the economic indicators, economists had expected the housing and automobile industries to be strong because of the recent declines in interest rates, which affect those purchases more than many others.

However, economists said the effect of interest rate declines has been offset by an increasing inflow of imports in the case of cars. In the case of housing, economists believe there are few new buyers for homes because mortgage rates are still at historically high levels, despite declines in interest rates.

The recent economic data make it appear less likely that the administration is going to get the 5 percent growth rate in the second half that it expected.

Private economists now say the economy will grow at a rate between 2.5 percent and 3 percent, not enough to keep the federal budget deficits from rising further or to lower the unemployment rate, they said.

"The more pessimistic estimates of economic growth in second half are going to come true," said James W. Christian, chief economist of the U.S. League of Savings Institutions.

Increases in the gross national product, the nation's output of goods and services, "will run from 2 to 3 percent instead of the 3 to 4 percent" many forecasters had been hoping for, Christian said.

"It's very depressing, isn't it?" said Lawrence Chimerine, chairman of Chase Econometrics Inc. "The slowdown in real income growth, widening trade deficits . . . profits are soft. These are not the conditions under which you can get an economic boom."

"We're not getting much rise in housing starts because unemployment is high, income growth is slow, multifamily construction is overbuilt," said Chimerine. He also said he didn't expect a recession, "but if we don't start to see some improvement in these numbers in the next month or two, we're going to have to start worrying about a recession."

A recession could occur as a result of imports continually eating away at domestic production and markets of U.S. firms, or it could come from a gradual decline in consumer spending, Chimerine said. Already, for the past two months, retail sales have dropped an average 1 percent and automobile sales have slumped, forcing General Motors to offer its lowest automobile financing ever -- a 7.7 percent interest rate announced earlier this week.

When conditions stagnate, "it's not hard to drop into recession," Chimerine said. "After that, it tends to feed on itself."

The one positive sign continues to be a moderate inflation rate that has not picked up appreciably since the recovery began almost three years ago. However, even the inflation picture has a down side, as prices of commodities such as farm products continue to plummet.

The Reagan administration and some private economists had said they expected the rebound to come chiefly from businesses rebuilding their stocks. In the first half of the year, businesses tried to get rid of inventories that had piled up as a result of slow demand.

After the inventory depletion, businesses would increase production later this year as they begin to rebuild their stocks, economists said. However, last month business sales plunged, marking the second-largest decline ever, and inventories rose, suggesting that businesses may still try to trim inventories and that factories won't pick up production in the next few months after all.

On the housing front, privately owned units were started at a seasonally adjusted annual rate of 1.7 million units, about the same level as for the past year. Housing starts last month were 6.5 percent below their average in the second quarter. For the first seven months of 1985, housing starts were 6 percent below the same period last year.

"Commitment rates on conventional long-term mortgages have edged up since early July, but they remain almost 2.5 percentage points below their peak in mid-1984," said Commerce Secretary Malcolm Baldrige. "Good levels of consumer confidence and small increases in new home prices relative to other price increases should support renewed improvement in starts during the next few months. Strong growth in home-building activity would require further reductions in financing costs."

The number of building permits issued last month for housing units dropped 0.9 percent. During the first seven months of the year, 4 percent fewer permits were issued than during the same period last year, the Commerce Department reported.