Public Citizen (search) charged that the two drugs increase the likelihood of heart attack.
Celebrex and Bextra are part of the family of drugs known as COX-2 inhibitors (search). Another drug in that group, Vioxx, was withdrawn last fall by its manufacturer, Merck & Co., because of heart problems.
Similar concerns have been expressed about Celebrex and Bextra, but they remain on the market.
Neither the FDA not the drugs' maker, Pfizer Inc., responded immediately to requests for comment on Public Citizen's petition.
COX-2 inhibitors have been widely popular for use as pain killers and anti-inflammatory drugs with fewer stomach and intestinal side effects than such products as aspirin.