WASHINGTON (Reuters) - Growth in U.S. factory activity slowed more than expected in September even as hiring in the private sector accelerated, signs of an uneven expansion in the U.S. economy.

The Institute for Supply Management said on Wednesday its index of national factory activity dropped to 56.6 last month, its lowest level since June, from 59.0 in August. Economists had forecast it would slide to just 58.5.

A gauge of new orders fell to 60.0 from 66.7.

Analysts have warned that U.S. factories could feel a chill from soft demand in the global economy and from recent strength in the dollar, and the ISM data could be a harbinger.

Still, gauges of U.S. manufacturing activity remain historically strong, with the ISM index still comfortably above the 50 mark that separates expansion from contraction - a sign the economy is still moving forward with strength.

Analysts believe U.S. gross domestic product is growing much more quickly than its 2.2 per cent average over the last two years, and the data did little to knock that view.

"It still looks as though overall GDP growth in the third quarter was around 3.5 per cent," said Paul Dales, an economist at Capital Economics in London.

There were some signs of cooling in the auto sector last month. U.S. auto sales in the third quarter were the best in eight years, but mixed September results from leading automakers indicated the industry's torrid summer pace is slowing.

A report from major payrolls processor ADP showed U.S. private employers added 213,000 jobs in September, just above economists' expectations. "Job gains remain strong and steady," said Mark Zandi, chief economist at Moody's Analytics, which co-developed the report.

The ADP figures come ahead of the government's more comprehensive payrolls report due on Friday, which includes both public and private-sector employment. That report is expected to show the economy added 215,000 jobs last month.