New orders for U.S. factory goods rose for a third straight month in September, but a further decline in order books suggested the manufacturing sector will struggle to emerge from a prolonged slump.

The Commerce Department said on Thursday new orders for manufactured goods increased 0.3 percent after an upwardly revised 0.4 percent gain in August.

Economists polled by Reuters had forecast factory orders rising 0.2 percent in September after a previously reported 0.2 percent increase in August. Unfilled orders at factories fell for a fourth straight month in September.

Manufacturing, which accounts for about 12 percent of the economy, has been hurt by a strong dollar and weak global demand. Production has also been undermined by the collapse in oil drilling activity in the aftermath of the plunge in oil prices.

There is cautious optimism, however, that a turnaround may be imminent. A survey published on Tuesday showed factory activity rising in October for a second straight month amid a jump in production.

But factories reported a slowdown in new orders, which suggests any pickup in manufacturing activity will be modest.

In September, orders for transportation equipment fell 1.1 percent, largely reflecting a drop in defense aircraft orders.

Motor vehicle production jumped 2.6 percent, the largest increase since July 2015. Orders for machinery increased 1.1 percent, the biggest rise since January.

The Commerce Department also said orders for non-defense capital goods excluding aircraft - seen as a measure of business confidence and spending plans – fell 1.3 percent instead of the 1.2 percent decline reported last month.

Shipments of these so-called core capital goods, which are used to calculate business equipment spending in the gross domestic product report, increased 0.4 percent in September instead of the previously reported 0.3 percent rise.

Shipments of overall factory goods shipments increased 0.8 percent, the biggest rise since June 2015. Inventories of factory goods were unchanged after two straight months of increases. That left the inventories-to-shipments ratio at 1.34 compared to 1.35 in August.

(Reporting by Lucia Mutikani; Editing by Paul Simao)