The Markit purchasing managers' index (PMI) for manufacturing activity fell to 51.1 from 51.5 in August, indicating that growth in the sector is slowing.
The PMI measure for the third-quarter was also at a three-year low.
Other PMI surveys released earlier on Monday also showed weak manufacturing readings for Europe, the UK and China.
Markit chief economist Chris Williamson said the US PMI reading indicated weakness in the sector was likely to be affecting the wider economy.
"Economic growth... looks to have slowed further from the 1.3% annualised rate seen in the second quarter, possibly even stagnating," he said.
Weak overseas demand saw new orders for exports slip at their fastest rate in 11 months.
Earlier, eurozone PMI figures had shown that the downturn in the manufacturing sector there had eased slightly in September.
The Markit Purchasing Managers' Index (PMI) for the eurozone region was 46.1 in the month, up from 45.1 in August. A score below 50 indicates contraction.
Manufacturing in the eurozone has now contracted for 14 consecutive months.
Factories across the eurozone reported weaker demand in domestic markets, while export orders also fell.
"Despite seeing some easing in the rate of decline last month, manufacturers across the euro area suffered the worst quarter for three years in the three months to September," said Mr Williamson.
"The survey is consistent with manufacturing output falling at a quarterly rate of perhaps as much as 1%, which means the sector will act as a severe drag on economic growth."
In the UK, the PMI survey indicated that manufacturing output shrank during September.
The Markit Purchasing Managers' Index (PMI) for the UK manufacturing sector fell to 48.4 in September from an upwardly revised 49.6 in August.
China's PMI manufacturing data showed that the sector had shrunk for a second month, although at a slower rate.
The country's PMI reading rose to 49.8 in September from 49.2 in August, government data showed.
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