The cost of employer-sponsored family health insurance rose a moderate 4 percent over the past year, a sharp slowdown from the surges in premiums that were typical before the recession but still faster than workers’ wages and inflation, according to a report released Tuesday.

The average premium for coverage for a family of four increased to $15,745, according to an annual survey of employers by the nonpartisan Kaiser Family Foundation. During the same period, workers’ wages rose 1.7 percent and inflation climbed 2.3 percent.

“Four percent is a low increase, and it is good news,” said Drew Altman, president and chief executive of the foundation.

But he added that it “doesn’t feel that way to working people,” because over the past decade, employee premiums for family coverage have risen 103 percent.

The bulk of the premium increases occurred in the early 2000s, before the economic downturn, with the cost of family plans rising 50 percent from 2002 to 2007. By contrast, premiums rose 30 percent from 2007 to 2012.

Researchers don’t know the exact reasons for the slowdown in premium growth, although many suspect that the recession and the sluggish recovery have prompted many families to put off non-emergency care to save money. And that trend probably has been encouraged by the growing number of employers that have shifted workers into plans with larger deductibles and co-pays.

But Altman said there is not enough evidence to say for sure, raising a host of questions: “Is this mostly the effect of the recession, or is there something else going on in health care to hold down costs? Will costs jump back again as they have in the past after periods of slower growth? Certainly you’d expect that — but by how much? We’ll have to wait and see.”

A report by the consulting firm Mercer, also released Tuesday, suggests that the moderate growth in premiums will at least extend through 2013. Mercer said early responses to its own annual survey of employers indicate that average premiums will rise about 6.5 percent next year.

The results of the Kaiser survey also reflect some early effects of the 2010 health-care law. For example, the report estimated that 2.9 million young adults are receiving coverage under a parent’s plan as a direct result of the legislation, up from 1.3 million last year. The reason: a provision in the law that requires employers to allow children to stay on their parents’ plans up to age 26.

The Kaiser report also found that, as expected, the share of workers in plans that are exempt from key provisions in the health-care law — because they are “grandfathered” — declined from 56 percent to 48 percent.

Grandfathered plans do not have to comply with a range of requirements, such as providing external appeals processes and covering preventive services without imposing out-of-pocket charges on patients. Plans lose their grandfathered status if they substantially increase employee costs or make significant changes to their benefit packages.

Two other provisions that have kicked in did not appear to play a big role in restraining premium growth: new rate-review rules requiring insurers to publicly justify large premium increases, and the “medical loss ratio” rule, which limits the share of premiums that insurers can keep as profit or use for administrative costs.

The Obama administration, in a new estimate Tuesday, said the rate-review rules have helped save American consumers an estimated $1 billion, while the medical loss ratio rule will require insurers to refund an additional $1.1 billion to nearly 13 million consumers this year.

But the Kaiser researchers noted that neither provision applies to self-insured employer plans, in which employers assume the financial risk for covering their workers. And about 60 percent of covered workers are in partly or completely self-funded plans.

In keeping with previous findings, the Kaiser report underscored the disparities in coverage among workers of different incomes.

Employees of firms that have a significant share of low-wage workers pay an average of $1,000 more each year for family coverage than those at higher-wage firms. Lower-income workers are also more likely to face high deductibles; 44 percent are in plans with deductibles of $1,000 or more, compared with 29 percent at higher-wage firms.

“Firms with many lower-wage workers ask employees to pay more out of pocket than firms with many higher-wage workers, even though the coverage itself tends to be less comprehensive,” said Gary Claxton, lead author of the Kaiser study.