WASHINGTON – American workers and their employers saw another rise in health insurance premiums this year, as the total cost of employer-provided health benefits ticked up 4 percent for family plans and 5 percent for individual plans, according to a closely watched national survey.

The 2013 increases are lower than in many previous years, undercutting claims by critics of President Obama’s health care law that the 2010 legislation is dramatically driving up costs.

Nor is there much evidence that many employers are dropping coverage — 57 percent of firms with at least three employees offered health benefits in 2013, according to the report by the nonprofit Kaiser Family Foundation and the Health Research & Educational Trust. The report’s authors noted that is “statistically unchanged” from 2012, when 61 percent of employers offered health benefits, and 2011, when 60 percent of employers did so.

But, as has been true in most previous years, the rise in premiums outpaced inflation and wage growth, adding to the increasing burden that health care costs are putting on Americans.

“It’s still three or four times the general rate of inflation,” said Helen Darling, president of the National Business Group on Health, a leading association of large employers. “We don’t consider (the increase) modest at all.”

The average total cost for a family health plan — which in most cases is split between employer and employee — hit $16,351 this year. The typical employee’s share of that premium hit $4,565, up about 6 percent from 2012.

The average employer’s share of the premium, in contrast, increased just 3 percent, an indication that employers continue to shift more health costs onto their employees.

The survey did not measure premiums for the roughly 20 million people who buy health insurance on their own; this group is dwarfed by the more than 150 million people who get employer-sponsored coverage.

Starting in October, Americans who do not get health benefits through their employer will be able to shop for health plans on new Web-based marketplaces created by the Affordable Care Act. Low- and moderate-income consumers will qualify for federal subsidies to offset their premiums.

Obama once promised that his law would reduce Americans’ health costs.

The Kaiser survey is the latest indication that that is not happening yet. In addition to rising premiums, workers also are getting hit with more cost-sharing, the survey found. For example, the average deductible for a health plan that covers only the employee reached $1,135, up from $1,097 in 2012.

Particularly hard hit are workers at small businesses, who already pay more for their health coverage than employee of large firms. Nearly a third of workers at employers with fewer than 200 employees have deductibles of at least $2,000.

Employers with more lower-wage workers also force their employees to pay more for their health benefits. Workers at firms where at least 35 percent of the workforce earns less than $23,000 pay $1,363 more for an average family plan than workers at firms with fewer low-wage employees, the survey found.

The 2013 rise in insurance premiums nonetheless is markedly lower than a decade ago, when double-digit annual increases were the rule. As recently as 2011, the average cost of a family plan surged 9.5 percent.

“This is good news for Obamacare because critics won’t be able to blame big premium increases on Obamacare because there aren’t any,” said Kaiser Family Foundation President Drew Altman.

The relatively modest premium increases also track other data showing a historic slowdown in health spending, which many experts believe reflects changes brought on in part by the 2010 health care law.