"The global manufacturing PMI looks to have bottomed in recent months," said David Hensley, director of global economics co-ordination at J.P. Morgan.
"While the current level is consistent with sluggish ... growth, conditions are in place for an acceleration in coming months, including solid demand growth and lean inventory positions," he added.
The new orders index slipped to 53.6 in January from December's 55.0. The output index, meanwhile, edged up to 54.0 from 53.5 with output growth in the United States rising at the fastest rate in three months.
The employment index also rose, to 51.9 from 50.7, while the input prices index fell for the third month running to 66.7 - its lowest level for almost a year.
National PMI surveys released on Tuesday showed a mixed picture. Euro zone manufacturing growth accelerated for the second consecutive month as stronger global demand boosted exports and domestic demand improved, but costs remained high.
A companion survey, released on Monday, showed manufacturing growth rose in Japan as demand from China strengthened.
But US manufacturing growth slowed in January as demand for new products eased. The headline index from the Institute for Supply Management slipped to 56.4 from a revised 57.3 in December, and was below the consensus forecast of 57.0.
High oil prices also weighed on manufacturers in Britain, where growth slowed to 51.8 in January from a revised 53.3 in December.