It also recommends, however, that these women avoid four types of fish entirely—shark, swordfish, king mackerel, and tilefish from the Gulf of Mexico—because the mercury content in them is too high. Plus, they recommend eating no more than six ounces of white tuna per week.
http://www.womenshealthmag.com/mom/should-pregnant-women-eat-canned-tuna
Looking at that data, they identified about 20 types of seafood that pregnant women can eat without issue, but they disagreed with the FDA and EPA's stance on tuna: They don’t think pregnant women should eat any.
http://www.womenshealthmag.com/mom/should-pregnant-women-eat-canned-tuna
Remember that fresh tuna is an oily fish, so if you eat two fresh tuna steaks in one week, you shouldn't eat any other oily fish that week. Tinned tuna doesn't count as oily fish, so you can eat this on top of the maximum of two portions of oily fish (as long as it's not fresh tuna or swordfish).
https://www.netmums.com/coffeehouse/pregnancy-64/netmums-52/132077-can-i-eat-cod-tuna-how-often-all.html
In 2004, the FDA urged women and young children to eat no more than 12 ounces of a variety of fish and shellfish with lower levels of mercury (including canned light tuna) or 6 ounces of white tuna (albacore) per week to minimize mercury risks.
http://www.webmd.com/baby/news/20060605/canned-tuna-avoid-pregnant
MORE: The 5 Fish That Are the Most Contaminated—and 5 You Should Eat Instead. So, um, can pregnant women eat tuna? We asked women's health expert Jennifer Wider, M.D., for her take, and she sides with the FDA and EPA on this one, though she says that it ultimately comes down to personal preference.
http://www.womenshealthmag.com/mom/should-pregnant-women-eat-canned-tuna
Consumer Reports urged women of childbearing age to limit tuna consumption to about three chunk-light cans per week or one can of white tuna (albacore) or solid-light tuna, since mercury can linger in the body even after you are no longer eating it.
http://www.webmd.com/baby/news/20060605/canned-tuna-avoid-pregnant
But like most fish, tuna contains traces of mercury. For this reason, the U.S. Food and Drug Administration (FDA) recommends certain people limit their intake of certain fish, including tuna. The amount of canned tuna you can eat every week depends on your physical condition and the type of tuna you choose.
http://www.livestrong.com/article/365763-how-much-canned-tuna-can-i-eat-every-week/
These people can eat up to 12 ounces of low-mercury fish per week; canned chunk light tuna can make up some or all of these 12 ounces If you eat canned albacore tuna, limit your intake to 6 ounces per week if you fall into one of the vulnerable population categories. Considerations.
http://www.livestrong.com/article/365763-how-much-canned-tuna-can-i-eat-every-week/
June 5, 2006 -- Recommendations published in the magazine Consumer Reports this week urge women to avoid eating any canned tuna while pregnant because of uncertainties about the risk of mercury contamination to developing fetuses.
http://www.webmd.com/baby/news/20060605/canned-tuna-avoid-pregnant
You should also limit the amount of tuna you eat to no more than two tuna steaks (weighing about 140g when cooked, or 170g raw) or four medium-size cans of tuna a week (with a drained weight of about 140g per can). This is because these fish contain more mercury than other types of fish.
https://www.netmums.com/coffeehouse/pregnancy-64/netmums-52/132077-can-i-eat-cod-tuna-how-often-all.html
how often to eat tuna
Eat four medium size cans of tuna a week.