When it comes to retirement, Americans are concerned most about high medical expenses, according to a new Bankrate.com report in which 28 percent of respondents cited that as their biggest worry.

Many millennials are concerned about planning for retirement. (John Wohlfeil, ThinkStock)

The highest-income households, which make more than $75,000 a year, were more concerned than the overall population. The biggest fear for millennials, 19-to 29-year-olds, was running out of money, which came in at a close second overall.

"People over 65 were twice as likely to mention medical expenses as their biggest fear compared to millennials," said Sheyna Steiner, senior investing analyst at Bankrate.com.  "For the higher income households, that might be because of the fact that they would have a harder time qualifying for medicaid should they have a catastrophic illness or injury that would require a lengthy nursing home stay.  That could wipe out a significant chunk of savings."

Other findings:

  • One-third say they can't save more for retirement because they have just enough money for the day-to-day expenses;
  • 14 percent blame other family obligations;
  • 10 percent lay fault with their student loan debt;
  • 29 percent are satisfied with the amount they are currently saving.

According to the survey, most are realistic about the role Social Security will have in their retirement:

  • 13 percent expect it to account for all or most of their retirement income;
  • 14 percent expect it to account for half of their retirement income;
  • 1 in 4 believe they won't get anything.

"The average Social Security payout is only around $15,000 per year, so people are realistic to think they'll need to supplement that income," Steiner said. "But despite all the gloom and doom about the future of Social Security, most Americans are optimistic that they'll get at least something from the program. That even includes millennials, 63 percent of them believe Social Security will fund at least some of their retirement several decades from now."