The Purchasing Managers Index for non-manufacturing businesses slipped from 53.7 to 52.2, indicating the rate of expansion slowed in the month, yet still grew, as numbers above 50 indicate expansion, while below 50 indicates contraction.
Slower expansion was also seen in the indexes for new orders and supplier deliveries, while new export orders fell into a contraction at 47.5, the institute said.
But indexes measuring the number of employees, inventories, backlogs of orders and prices all expanded, showing faster growth.
The institute said 14 of 18 service-oriented industries showed growth in the quarter. The fasted growth was noted by management of companies in arts, entertainment and recreation, as well as transportation and warehousing.
Mining, education, healthcare and social assistance and other services contracted in June.