The headline index (the Purchasing Managers' Index) rose from 49.7 in June to 49.8 in July, still falling short of 50, which is the dividing line between contraction and growth.
The index indicates "contraction in the manufacturing sector for the second consecutive month following 34 consecutive months of expansion," the report said.
The institute said seven of 18 manufacturing groups showed growth in July, down from 13 in May. The strongest growth was seen in plastics and rubber products, electrical equipment, appliances and petroleum and coal.
The component index for new orders rose from 47.8 to 48. The employment index showed growth slowing with the index remaining above 50, but dropping from 56.6 to 52.
The prices index, which has dropped sharply, changed direction, rising from 37 to 39.5.
The export index showed steeper contraction at 46.5, falling from 47.5. The index for imports showed growth at 50.5, but at a slower pace than June, when the index rested at 53.5.