It stopped short of calling for drugs, which are also being scrutinized by the U.S. Food and Drug Administration, to be taken off the market.
The agency issued a new warning that those who had suffered heart disease or strokes should not take any Cox-2 drugs, and those with uncontrolled high blood pressure should not take the medication etoricoxib, which is sold under the trade name Arcoxia by Merck & Co.
It urged doctors to use care when prescribing Cox-2 painkillers to patients who have risk factors for heart disease, including high blood pressure, high cholesterol, diabetes and smoking.
The agency also said that given the risks, doctors should prescribe the lowest effective dose for the shortest possible time for all patients.
The European agency last reviewed Cox-2 drugs in 2003.