“The additional risk is relatively small, but it could be the straw that breaks the camel’s back for someone already at risk,” Professor Lambert said. The evidence that the drugs increase the risk of heart attack, stroke and heart failure “is now extremely solid,” he said.

“I don’t think we will ever see a study that says, ‘Oops, Nsaids were safe after all,’ ” he added.

The agency said it would ask drug manufacturers to change the labels to reflect new evidence that the drugs increased the risk of heart attack and stroke soon after patients first started taking them, and that while the risk was higher for people with heart disease, it surfaced even for people who had never had heart problems.

Dr. Peter Wilson, a professor of medicine and public health at Emory University in Atlanta, was a member of an expert panel convened by the F.D.A. last year to sift through new evidence on the drugs, including a meta-analysis of a number of scientific trials, as well as some observational studies. He offered a rule of thumb for the scale of risk based on studies he and others reviewed last year.

The over-the-counter medications, which have the lowest doses, probably increased risk by about 10 percent, he said. Low-dose prescription medications were likely to increase the risk by about 20 percent and higher-level dose prescription medications by about 50 percent, Dr. Wilson said. He emphasized that there was significant variability in each estimate. For example, the risk for the over-the-counter drugs might be zero or might be 20 percent.

“There is great concern that people think these drugs are benign, and they are probably not,” he said. “The thought is these are good for short-term relief, probably for your younger person with no history of cardiovascular trouble.”