Sometimes, but only with your prescriber's sign-off: fish oil can mildly thin the blood on its own, so combining it with a blood thinner can add to bleeding risk — clear it with your doctor or pharmacist first and don't start it on your own.
The omega-3 fats in fish oil (EPA and DHA) have a mild blood-thinning effect of their own — NCCIH notes that omega-3 supplements "may extend the time it takes for a cut to stop bleeding" and that people taking "blood thinners" or NSAIDs "should discuss the use of omega-3 fatty acid supplements with a health care provider." Stacked on top of a prescription anticoagulant (such as warfarin) or antiplatelet (such as aspirin or clopidogrel), that effect can be additive — which is why NIH's Office of Dietary Supplements warns that "high doses of omega-3s may cause bleeding problems when taken with warfarin (Coumadin) or other anticoagulant medicines." Blood thinners like warfarin have a narrow safety margin and are closely monitored, so any new supplement needs to be checked first. This is why authoritative sources (NCCIH, NIH ODS, NHS) tell people on blood-clotting medicines to discuss supplements with their clinician before starting — the NHS specifically advises telling your doctor or pharmacist about any "herbal remedies, vitamins or supplements" before taking warfarin or apixaban.
Tell your prescriber or pharmacist before adding fish oil, and let your anticoagulation clinic know — warfarin in particular is closely monitored with INR blood tests, and they may want to recheck after you start. Keep marine omega-3 (EPA+DHA) modest: NIH ODS notes the FDA recommends consuming no more than 5 g/day of EPA and DHA combined from supplements, and bleeding concern rises with higher "mega-dose" amounts, so don't exceed the label or your doctor's advice. Watch for warning signs of bleeding and get medical help if they appear: unusual or easy bruising, frequent nosebleeds, bleeding gums, blood in your urine or stool (or black/tarry stools), coughing up or vomiting blood, or a sudden severe headache with confusion or slurred speech (call 911 / NHS 111). Higher-risk people — anyone on warfarin, a DOAC (apixaban, rivaroxaban), aspirin, clopidogrel, or other antiplatelets, those with a bleeding disorder, or anyone scheduled for surgery — should be especially careful and may be told to pause fish oil before a procedure. Also note prescription-strength omega-3 (e.g. Lovaza, Vascepa) is a higher dose than a typical supplement and is managed by your doctor. If you're pregnant, nursing, or allergic to fish or shellfish, check first too.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.