WASHINGTON -- There may be more mercury than the law allows in that swordfish at the grocery store.

A University of North Carolina lab study found elevated mercury concentrations in 24 swordfish samples from supermarkets in 22 states. The samples came from chains including Safeway, Shaws, Albertsons and Whole Foods.

Groups that paid for the analysis, including Oceana and the Mercury Policy Project, want supermarkets to post signs warning shoppers of the health risks from mercury. They also want the Food and Drug Administration to step up their testing.

Scientists found an average mercury concentration of 1.1 parts per million (ppm) in the swordfish samples tested. That level exceeds the FDA Action Level of 1.0 ppm for commercial fish, which is the amount at which the agency can take legal action to remove a product from the market.

Two samples, including one from Maine and one from Rhode Island, contained more than 2 ppm, twice the FDA Action Level, according to a news release from the Mercury Policy Project.

The American Heart Association advises people to eat fish at least twice a week. However, the federal government warns pregnant women, nursing mothers and young children to avoid fish with high levels of mercury. Those would be shark, swordfish, king mackerel or tilefish.

"Pregnant women and parents of young children need point-of-sale warnings to make informed choices about the fish they purchase," said Michael Bender, director of the Mercury Policy Project.

The government advises eating shrimp, salmon, pollock, catfish and canned light tuna.

• Full Report: Mercury Policy Project