In a formal petition to the U.S. Food and Drug Administration, Public Citizen said the two drugs' potential to cause heart attacks and strokes outweighed any possible benefit.
The letter, a copy of which was obtained by Reuters, is the latest action following a series of warnings over heart problems connected to both prescription and over-the-counter painkillers.
Merck Inc. pulled its arthritis drug, Vioxx, from the market in September after a study showed its doubled the risk of heart attack and stroke.
Last month, the National Institutes of Health halted two studies involving Celebrex and naproxen, a nonprescription painkiller sold as a generic and under several brand names, including Bayer AG's Aleve and Roche AG's Naprosyn.
Pfizer has kept Celebrex on the market but agreed to suspend consumer advertising.
It also placed a note on Bextra warning of increased risk in patients who have just had heart bypass surgery.
The FDA has called on doctors to limit prescribing of Celebrex and Bextra, and an FDA advisory panel of outside experts plans to meet for an unusual 3-day meeting to discuss the entire class of drugs.
In its letter sent Monday, Public Citizen said Pfizer's drugs have not been proven any safer than older non-steroidal, anti-inflammatory painkillers, known as NSAIDs, like aspirin or naproxen.
Public Citizen researchers analyzed results from 14 randomized trials involving all drugs in the class that includes Celebrex and Bextra -- known as Cox-2 inhibitors.
Arcoxia is approved in the European Union, but the FDA rejected the experimental drug in October, requesting more data.
Novartis pulled its application for EU approval in November, saying it would provide more data, and has said it is working to get the drug approved in the United States.