Consumers may want to rethink popping fish oil pills if they're hoping those supplements full of omega-3 fatty acids will keep their brains healthy.

A new study--one of the largest and longest in duration of its kind--finds that taking omega-3 supplements did not slow cognitive decline among 4,000 participants.

"The supplements just don't cut it," said Elizabeth Chew, deputy clinical director at the National Eye Institute, part of the National Institutes of Health. "If people are thinking [taking them] is going to help cognitive function, it's not going to do so among the older age group."

A much better bet for all-around brain and heart health, she said, is eating foods naturally high in omega-3 fatty acids, such as salmon, flaxseed and walnuts.

Omega-3 supplements are available over the counter and often promoted as enhancing brain health. Fish oil pills are among the most popular dietary supplements in the United States.

In the study, Chew and her team enrolled participants who were at risk for developing age-related macular degeneration, a major cause of vision loss among older Americans. They were investigating the possible cognitive benefits of omega-3 supplements.

The participants were randomly assigned to one of four groups. At the beginning of the study, they were tested on their immediate recall, attention and memory, and then tested two and four years later.

Researchers said they found that taking the omega-3 supplements had "no statistically significant effect on cognitive function."

Researchers were quick to point out that the study, published in the Journal of the American Medical Association, only looked at the impact of supplements, not foods high in omega-3 fatty acids.

Their study was also limited to older participants, with an average age of 73.

"We don't know whether these supplements might be beneficial at an earlier age," Chew said. "At 73, it's very hard to turn the clock back."

There have been many observational studies linking omega-3 fatty acids to brain health, she said, but few randomized clinical trials.

A large 2011 study found that omega-3 supplements did not improve the brain health of older patients with pre-existing heart disease, she said.