WASHINGTON, Sept 2 (Reuters) - New orders for U.S. factory goods recorded their largest increase in nine months in July as demand increased broadly, in a hopeful sign for the embattled manufacturing sector.

The Commerce Department said on Friday that new orders for manufactured goods rebounded 1.9 percent after a downwardly revised 1.8 percent decrease in June. It was the biggest rise since October 2015 and followed two straight months of declines.

Economists polled by Reuters had forecast factory orders rising 2.0 percent in July after a previously reported 1.5 percent decline in June.

The department also said orders for non-defense capital goods excluding aircraft increased 1.5 percent in July instead of the 1.6 percent rise it reported last month. These so-called core capital goods are seen as a measure of business confidence and spending plans on equipment.

Core capital goods shipments, which are used to calculate business equipment spending in the gross domestic product report, fell 0.5 percent in July. They were previously reported to have slipped 0.4 percent in July.

Manufacturing, which accounts for about 12 percent of the economy, remains constrained by the lingering effects of a strong dollar and weak global demand, which have crimped exports of factory goods.

A collapse in oil drilling activity following a plunge in oil prices has also squeezed manufacturing by undermining business spending, leading to weak demand for heavy machinery.

In addition, a U.S. inventory correction has resulted in factories receiving fewer orders. The Institute for Supply Management reported on Thursday

that its national factory activity index fell into contraction territory in August for the first time in six months.

In July, orders for transportation equipment surged 10.6 percent, also the biggest gain since last October. Orders for motor vehicles and parts slipped 0.5 percent.

Orders for machinery, which have been hurt by weak demand in the energy, mining and agricultural sectors, jumped 1.4 percent - the largest rise in six months.

Orders for electrical equipment, appliances and components soared 3.7 percent, the biggest gain since June 2014. Orders for computers and electronic products rose 3.4 percent, the largest rise since March 2015.

Inventories of factory goods edged up 0.1 percent after 12 straight monthly declines. Shipments slipped 0.2 percent. As a result, the inventories-to-shipments ratio was unchanged at 1.35 in July.

Unfilled orders at factories decreased for a second straight month.

(Reporting By Lucia Mutikani; Editing by Andrea Ricci)