New orders for manufactured goods rose 0.7 percent in September to a seasonally adjusted $155.5 billion on the strength of purchases of nondurable items such as petroleum products and chemicals, the Commerce Department said yesterday.

Separately, the Commerce Department reported that the rate of new-home sales leaped by a stunning 24 percent from August to September.

In the report on factory orders, the department said that orders for durable goods fell by 0.1 percent to a level of $72.9 billion, a downward revision from a 0.2 percent increase reported earlier on the basis of less complete data.

Shipments of nondurables rose by $1 billion to $82.4 billion, while those of durables fell by $1.1 billion to $76.2 billion. The offsetting movements, coupled with the new orders, left the factory-order backlog at $296 billion, down $3.1 billion, or 1 percent, for the month. It was the 14th consecutive monthly decline.

New orders for nondefense capital goods rose $900 million, or 4.7 percent, to $19.8 billion. At that level, however, orders were still below the July level of $20.3 billion.

Shipments of durable goods fell 1.4 percent in September following a 2.3 percent drop in August. Transportation equipment showed the largest decline in September, down $1.4 billion to $16.2 billion.

The book value of manufacturers' inventories fell $2.2 billion to a level of $272.2 billion. The 0.8 percent decline was the ninth drop in the last 10 months.

The department reported that September new-home sales, spurred by recent declines in mortgage interest rates, shot up to an annual rate of 464,000. This was 39 percent higher than September 1981, when sales hit a record-low level of 335,000 a year.

Over the past year, inventories have dropped from an 11.7 months' supply to 7.1 months.

Most of the improvement was in the South and Northeast, with sales in the West dropping and sales in the North Central area rising only slightly.

The South is "where the jobs are," said Mark Riedy, executive vice president of the Mortgage Bankers Association, predicting that future improvements would track employment. He also said the recovery would continue, and that the low level of inventories is particularly encouraging.

Lower interest rates are largely responsible for the sales gains, housing economists said. A year ago, the government-mandated FHA/VA rate hit a record of 17 1/2 percent; now it is 12 1/2 percent.