In almost all the 12 countries polled, three-quarters or more of respondents said people should be able to decide when and how they die.
Two-thirds to three-quarters of respondents said they could imagine opting for assisted suicide themselves if they suffered from an incurable illness, serious disability or uncontrollable pain.
The study was conducted by the Swiss Medical Lawyers Association (SMLA) in Austria, Britain, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Portugal, Spain and Sweden.
A minimum of 1,000 people in each country were surveyed.
In Britain, 71 per cent of respondents said they might seek assisted suicide if it were legal.