Research has suggested all painkillers in a class of drugs, including ibuprofen and naproxen, could be linked to an increased risk of heart attack.
The drugs are used to alleviate pain
The drugs belong to a family known as non-steroidal anti-inflammatories.
Last year, trials raised concerns over two NSAIDs and one of them, Vioxx, was taken off the market.
The authors of the study, in the British Medical Journal, said patients should not stop taking the drugs, but called for further investigations.
Some experts questioned the validity of the study findings, saying other factors might have caused the apparent increased heart risk.
The drugs are generally used by people who have chronic pain from conditions such as arthritis.
The two drugs covered by last year's trials were COX-2 inhibitors.
One extra patient for every 521 taking diclofenac was likely to suffer a first-time heart attack
One extra patient for every 695 taking rofecoxib was likely to suffer a first-time heart attack
One extra patient for every 1,005 taking ibuprofen was likely to suffer a first-time heart attack
They are more 'stomach friendly' alternatives to NSAIDs, which can sometimes cause ulcers and bleeding.
In the BMJ study, Professor Julia Hippisley-Cox and colleague Carol Coupland used a UK database of patients registered with a GP to identify any who had suffered a heart attack for the first time over a four-year period.
They then looked at what drugs these 9,218 patients had been taking, paying particular attention to NSAID use.
Compared with patients who had not had a heart attack, patients who had were more likely to have been taking any of four types of NSAID.
These included the two COX-2 inhibitors - Vioxx (rofecoxib)and Pfizer's Celebrex (celecoxib) - plus diclofenac and ibuprofen.
For ibuprofen, the odds increased by almost a quarter (24%), and for diclofenac it rose by over a half (55%). For celecoxib the odds increased by a fifth (21%) and for rofecoxib it rose by a third (32%).
But this translates into a low actual risk.
Therefore, one extra patient for every 521 patients taking diclofenac was likely to suffer a first-time heart attack.
For rofecoxib the figure was one patient for every 695 patients, and for ibuprofen one patient for every 1,005 patients.
Swiss medical experts from the University of Berne said in a BMJ editorial that the results should be interpreted with caution.
"The quality of the data on cardiovascular risk factors and other potential confounders was poor," they said.
The study authors admitted it was possible that other factors might have skewed their results, but they said they did take into account other heart disease risk factors such as smoking and obesity.
Lead author Professor Hippisley-Cox, from the University of Nottingham, said: "Enough concern exists to warrant a reconsideration of the cardiovascular safety of all NSAIDs."
UK drug regulators said they were reviewing the available evidence and would provide further advice as necessary.
"In the meantime, it is advisable to use the lowest effective dose of NSAID for the shortest time necessary," said the Medicines and Healthcare products Regulatory Agency.
It says COX-2s should not be prescribed in patients with established ischaemic heart disease, cerebrovascular disease or those with moderate heart failure.
Professor Peter Weissberg of the British Heart Foundation said: "It would be wrong to change clinical practice on the basis of current evidence."
He called for more safety investigations.
"For now, any patients who are prescribed NSAIDs should be reassured that the results indicated a very low incidence of heart attack.
"People may consider the possible slight increased risk to be acceptable when offset against the welcome pain relief that these medicines can offer."
A spokeswoman from Arthritis Research Campaign said: "It's very important that people don't panic; hundreds of thousands of arthritis patients take these drugs without problems or side-effects."
David Pruce from the Royal Pharmaceutical Society of Great Britain said: "This type of study is fraught with difficulties. We are concerned that too much credence may be given to this study, which may not be warranted.
The International Ibuprofen Foundation stressed that the study looked only at the drug used in high doses and for long durations and therefore that the findings did not in any way aplly to occasional use, at low doses, for minor ailments by the general public.
He advised patients against stopping NSAID therapy based on the findings.