UnitedHealth Group Inc. saw profits rise sharply because of savings from surgeries, hospital stays and doctor visits canceled amid the coronavirus pandemic, but the company said that health care returned to near-normal levels in recent weeks.

The second-quarter results from UnitedHealth, parent of the largest U.S. health insurer, UnitedHealthcare, offer one of the broadest pictures so far of the pandemic’s financial impact on the health sector. The company’s Optum arm also owns a sprawling network of surgery centers, doctor…