The ISM's manufacturing index rose to 56.4 from 56.2 in September. A reading above 50 indicates growth.
Factories also expanded in Europe this month, though at a slightly slower pace, according to surveys in that region. Manufacturing indexes have all picked up in China, Japan, and South Korea.
The overseas strength is boosting demand for U.S. factories. A measure of export orders jumped to its highest level in nearly a year and a half in October, the ISM report said.
"The outlook for manufacturing looks far more constructive now than it did over the past several months, in light of the improving global backdrop," said Michael Dolega, an economist at TD Economics.
U.S. factory activity has now risen at an increasingly fast pace for five straight months, according to the ISM's index. In October, a measure of new orders rose slightly. And a gauge of production fell but remained at a high level. Factories added jobs, though more slowly than in September.
The shutdown did depress activity at some companies that make metal products and electrical equipment. And while the survey's findings suggest stronger output in coming months, the most recent measures of factory production remain tepid.
"The strength of this hasn't yet been reflected in actual manufacturing output," said Amna Asaf, an economist at Capital Economics.
On Monday, the Federal Reserve said factories barely increased their output in September. Automakers produced more. But that gain was offset by declines at companies that make computers, furniture and appliances.
Companies reduced demand in September industrial machinery, electrical equipment and other core capital goods that signal investment, the government said last week. And August's figures those orders were revised down.
Economists pay particular attention to core capital goods, which exclude aircraft and defense-related goods, because they reflect business confidence.
Analysts were also encouraged by a survey of companies in the Chicago region, released Thursday. It found that the companies expanded at their fastest pace in more than two years in October. New orders jumped, and hiring also rose.
Still, economists don't expect manufacturing to boost economic growth in the coming months. Growth likely fell to a weak annual rate between 1.5 percent and 2 percent in the July-September quarter from a 2.5 percent pace in the April-June period.
Most economists expect similarly slow growth in the final three months of the year.
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