Short answer: Often, but it is worth telling your prescriber. The NIH Office of Dietary Supplements says fish oil can have antiplatelet effects at high doses and might raise INR with warfarin, but most research found 3 to 6 g a day did not significantly change anticoagulation. A 2014 review found no rise in clinically significant bleeding. Prescription omega-3 labels still say people on blood thinners should have INR checked periodically.
The NIH Office of Dietary Supplements (ODS) omega-3 fact sheet names warfarin (Coumadin) and similar anticoagulants as its example of a medicine interaction. Its points, in order:
Warfarin has a narrow window between too little effect and bleeding, and its dose is set from INR results. The MedlinePlus warfarin page tells patients to let their doctor and pharmacist know about all vitamins, nutritional supplements and herbal products, because some may increase bleeding risk. It lists several, including coenzyme Q10, garlic, ginkgo and ginseng, along with aspirin and NSAID pain relievers.
Fish oil is not on that MedlinePlus list, but the prescription omega-3 labels' INR monitoring line, as summarized by ODS, is why a prescriber may want to know about it. See vitamin K and warfarin for the dietary side.
The ODS fact sheet discusses warfarin and similar anticoagulants. It does not give data for newer anticoagulants such as apixaban or rivaroxaban, or for antiplatelet drugs such as clopidogrel, so this page cannot say how fish oil combines with them. Their labels and your prescriber or pharmacist are the place to check.
ODS lists commonly reported side effects of omega-3 supplements as usually mild: unpleasant taste, bad breath, heartburn, nausea, stomach discomfort, diarrhea, headache and smelly sweat. It also notes that two large trials found 4 g a day of omega-3s for several years slightly raised the risk of atrial fibrillation (an irregular heart rhythm) in people with or at high risk of heart disease.
The ODS findings are about grams of omega-3 fish oil, and capsule strengths vary. Useful notes for an anticoagulation visit: the product, how many capsules a day, the EPA and DHA content from the label, the date you started, and any unusual bruising or bleeding. Dose Track logs supplements with their amount alongside your INR results and warfarin doses.
Read more on Dose Track: Omega-3 fish oil guide · Krill oil · Cholesterol · Blood clots on TRT