The price of employer health insurance rose a modest 3 percent this year, a major survey shows, but workers will be paying more when they get sick as deductibles soar.

Annual insurance premiums for families increased 3 percent, on average, to $16,834, according to the survey released Wednesday by the Kaiser Family Foundation and the Health Research & Educational Trust.

Those results reflect a recent trend of slower growth in health care costs. But many employers and health-policy experts predict bigger increases for 2015 and beyond as the economy recovers.

“Large employers are skeptical the current low trends will continue for a variety of reasons,” said Bill Kramer, executive director for national health policy at the Pacific Business Group on Health, which represents large employers such as Boeing Co. and Walt Disney Co. “Historically, periods of slow growth have always been followed by rapid increases.”

Insurance offered by employers is the primary source of health coverage for Americans, providing benefits to about 150 million people. Most employers will begin open enrollment for 2015 plans in the coming weeks.

Even modest changes in medical costs have been difficult to absorb for many businesses and workers hurt by the Great Recession. And many employers have cut their financial exposure by placing a greater share of the costs on workers.

The average employee deductible has increased 47 percent since 2009 to $1,217 annually. Eighteen percent of workers face a deductible of at least $2,000. Workers typically must pay that amount before most medical services are covered by their health plan.

Some health-policy experts credit higher deductibles with helping hold down medical costs by discouraging people from getting care or motivating them to be savvier shoppers. But throwing up barriers to cost-saving preventive care is a potential downside.

“Higher deductibles may be good if you’re relatively young and healthy,” said Drew Altman, chief executive of the Kaiser Family Foundation. “But they may be a bad thing if you are lower or moderate income or chronically ill. This can be a real burden on the family budget.”

For a change this year, the growth in employer health premiums was close to the annual increase in workers’ wages at 2.3 percent and inflation of 2 percent.

However, the longer-term trend hasn’t been encouraging. Since 1999, workers’ share of health premiums has shot up 212 percent, nearly four times as fast as wage growth nationwide, the survey found.

In 2014, the average worker paid $4,823, or 29 percent, toward the $16,834 family premium. Workers contribute $1,081, or 18 percent, for the average employee-only premium of $6,025.

The survey found that 55 percent of U.S. firms offered health benefits to their workers, down from a recent high of 69 percent in 2010.

The offer rate is far higher among larger firms. The survey shows that 92 percent of employers with at least 50 workers already offer health coverage to at least some of their workers.

Starting next year, some larger businesses could face penalties under the Affordable Care Act if they don’t offer health benefits. Those health-law requirements do not apply to businesses with fewer than 50 full-time employees.