The recovery for U.S. services businesses gained momentum in September, surveys of purchasing managers show, while fresh coronavirus restrictions hurt activity in Europe and Asia.

The Institute for Supply Management’s nonmanufacturing index—a survey-based measure of activity in U.S. industries such as travel, health care, restaurants and real estate—rose to 57.8, up from 56.9 in August. Separately, private data firm IHS Markit said Monday its U.S. services index came in at 54.6 last month, down slightly from 55.0 in August…