Factory orders for durable goods fell 3.2 percent in June, the government said yesterday in a report that raised new concerns that the nation could be flirting with a recession.

Orders for durable goods are considered a key barometer for the future because a drop in orders normally triggers reductions in production plans and job layoffs.

The Commerce Department said that demand for durable goods -- long-lasting items such as appliances and battleships -- fell $4.14 billion to a seasonally adjusted $124.69 billion last month.

The June decline came as a surprise to analysts who had counted on a further pickup in orders to signal that the fortunes of the nation's manufacturing sector were on a permanent upswing.

Hopes for a rebound in manufacturing had been fueled by a 4.2 percent rise in orders in May and an even bigger 6.7 percent advance in March. But the June decline continues the saw-tooth pattern of 1990. Orders fell by 4.1 percent in April and dropped by a record of 10.5 percent in January.

''The durable goods report is a distinct yellow flag on how the economy might perform in the second half of the year,'' said Allen Sinai, chief economist of the Boston Co.

Mark Zandi, senior economist at Regional Financial Associates in Chester, Pa., said many economists had looked for a rebound in manufacturing to help bolster growth in coming months.

''If manufacturing doesn't show signs of strength, there really is no sector of the economy to provide the impetus for growth,'' he said. ''The consumer sector is extremely weak, investment spending has been hurt by the slide in profits and housing is in a recession.''

A separate report yesterday showed that sales of existing single-family homes posted a small 1.2 percent advance in June, the first monthly gain since last September.

The National Association of Realtors attributed the upturn to falling mortgage rates and said it offered the promise of further gains in the months ahead. But other economists said that a one-month upturn did not signal an end to the extended slump besetting the housing industry.

In a sign of how sluggish the manufacturing sector has been, orders for durable goods totaled $744.7 billion during the first six months of this year, 1.5 percent below the same period in 1989.