WASHINGTON — It sounds like good news: Annual premiums for job-based family health plans went up only 4 percent this year.

But hang on to your wallets. Premiums averaged $15,745, with employees paying more than $4,300 of that, a glaring reminder that the nation’s problem of unaffordable medical care is anything but solved.

The annual employer survey released Tuesday by two major research groups also highlighted another disturbing trend: employees at companies with many low-wage workers pay more money for skimpier insurance than what their counterparts at upscale firms get.

Overall, “it’s historically a very moderate increase in premiums,” said Drew Altman, president of the Kaiser Family Foundation, which conducted the survey with the Health Research & Educational Trust.

He quickly added: “But even a moderate increase feels really big to workers when their wages are flat or falling.” The rise in premiums easily outpaced workers’ raises and inflation.

Following a 9-percent hike in premiums last year, the 2012 increase quickly became fodder for the political debate. Republicans said President Barack Obama’s promises to control health-care costs ring hollow in light of the findings.

But the most significant cost-control measures in Obama’s law have yet to take effect, and the president’s big push to cover the uninsured doesn’t start until 2014. Those measures include a new tax on the most expensive insurance plans and a powerful board to keep Medicare spending manageable.

Trying to head off critics, the administration issued a report estimating that consumers have saved $2 billion as a result of the health-care law. That’s due to a combination of insurance rebates for employers and individual policy holders, as well as closer state oversight of proposed rate increases, facilitated by Obama’s law.

Still, the Kaiser survey shows premiums for job-based family coverage rose by nearly $2,400 since 2009 when Obama took office, with a corresponding increase of nearly $800 for employee-only coverage.

“We aren’t happy to see any increase in health insurance premiums,” said Gary Cohen, head of the administration’s Center for Consumer Information and Insurance Oversight, adding that officials are “heartened” it was only a modest rise this year and look forward to slowing costs as more provisions of the health-care law take effect.

Most independent experts say the fact that premiums keep rising faster than overall inflation reflects underlying problems with the health-care system that have frustrated policymakers of both parties for years, as well as corporate benefit managers.