Premiums for employer-provided health insurance have increased by relatively modest amounts this year, according to a new survey, a further sign that once-torrid health care inflation has abated for now.

The average annual premium for a family rose 4 percent in 2013, to $16,351, according to the survey results released Tuesday by the Kaiser Family Foundation. Annual premiums for individual policies purchased through an employer rose 5 percent, to $5,884.

The 4 percent increase for a family is relatively tame, at least compared with the roughly 10 percent annual increases experienced a decade ago. But it is still a far bigger rise than 1.8 percent increase in wages and the 1.1 percent rate of inflation in the last year, the foundation said.

“If you are comparing it to 10 years ago in health care, it seems modest,” said Helen B. Darling, chief executive of the National Business Group on Health, which represents large employers. “If you compare it to the economy and what inflation is doing, I don’t think it’s modest at all.”