European regulators have said patients who have had heart disease or a stroke should not take a common painkiller.
Cox-2s are used to treat pain and inflammation
The European Medicines Agency said doctors should also be "cautious" about giving Cox-2 inhibitors to patients who have risk factors for heart disease.
These can include high blood pressure, high cholesterol and smoking.
Patients in these groups who are already taking Cox-2s are do not need to stop taking them, but should discuss their treatment with their GP.
The news comes as the US Food and Drug Administration carries out its own investigation into the safety of Cox-2s.
'Lowest possible dose'
European experts say stopping Cox-2 therapy will not cause patients any harm, but said they were likely to need alternative treatment to relieve their symptoms.
COX-2 inhibitors are more 'stomach friendly' alternatives to traditional pain relief drugs called non-steroidal anti-inflammatory drugs (NSAIDs), which can sometimes cause side effects such as ulcers and bleeding.
They are used to treat pain and inflammation in arthritis and to relieve acute pain.
Around 1.4m people take the drugs in the UK.
In its review, the EMEA reviewed all the available data on the cardiovascular safety of Cox-2s.
The drugs which the EMEA looked into were Celebrex (celecoxib), Arcoxia (etoricoxib), Dynastat (parecoxib), Prexige (lumiracoxib) and Bextra (valdecoxib).
The EMEA's Committee for Medicinal Products for Human Use said: "The available data shows an increased risk of cardiovascular adverse events for COX-2 inhibitors as a class.
"The data also suggest an association between duration and dose of intake and the probability of suffering a cardiovascular event."
The EMEA advised doctors to prescribe Cox-2s for the shortest possible time at the lowest possible dose.
It also said that the drug etoricoxib (Arcoxia) should not be prescribed to patients with high blood pressure which was not under control.
Further advice will be published by the EMEA in April. The agency added that further research into the effects of Cox-2s was still needed.
The drugs it considered belong to the same class as the arthritis painkiller Vioxx, which was removed from the market in September last year because of safety concerns.
However Merck, the company which manufactured Vioxx, said it would consider selling the drug again if the Food and Drug Administration decided the cardiovascular risks associated with the medicine were similar to those of other Cox-2s.
A spokeswoman from the Arthritis Research Campaign, said the reputation of Cox-2s was now "irreparably damaged".
She added: "The number of heart attacks and strokes as a result of Cox-2 could have been avoided if pharmaceutical companies had been more open about their products' side effects when their drugs were launched, and if the drug regulatory bodies had acted more swiftly and with more rigour.
"Whatever happens now, the reputation of this class of drugs, once heralded as side effect free, have been irreparably damaged."
And a spokesman for the Stroke Association said: "We believe that there is growing evidence that these drugs raise blood pressure - a major risk factor for stroke.
"Last year Vioxx was withdrawn because of this risk. It is now time that the whole class of these drugs be withdrawn too."
Neil Betteridge, chief executive of the Arthritis Care charity, said: "It is still likely that many people currently taking certain brands of Cox 2 inhibitors will be concerned about what they should do next.
"As always, Arthritis Care would strongly advise anyone in the slightest doubt to consult their GP or health practitioner."