A poll has suggested that four out of 10 people in Scotland would break the existing law to help loved ones die.
The rules on assisting someone to die should change, says the poll
The Voluntary Euthanasia Society, which carried out the UK-wide interview of 790 adults, said the Scottish Executive should sponsor a debate on the subject.
But the long-held view of ministers has been that relaxing the law would weaken the protection to society.
Westminster is looking at a Euthanasia Bill, but it would not apply in Scotland as it is a devolved matter.
Dr Richard Simpson, a former Scottish minister, said it was time for a reasoned debate.
He said that the Adults with Incapacity Act (Scotland) 2000, which was one of the first pieces of legislation passed by the Scottish Parliament, promoted a very strong debate on euthanasia.
"There hasn't been a debate for the last four years because the issue was resolved and the wishes of parliament were made clear, but it is time for another debate," said Dr Simpson.
He pointed out that the current legislation provided terminally ill patients with a right to make "living wills".
POLL - SCOTLAND BREAKDOWN
39% said they were prepared to break the law to help a loved one die
82% support a change in the law on medically assisted dying
51% would want doctors and family to break the law
That comprises a set of rules about what a practitioner can or cannot administer.
A Scottish Executive spokesperson said that ministers had no plans to change the present law.
She added: "Our policy has been and remains that, while it is right that terminally ill patients should receive the best palliative care available, the deliberate taking of life cannot be condoned and should remain illegal."
Sheila McLean, who is professor of medical ethics at Glasgow University, said everyone had an entitlement to expect a level of "certainty, cogency and clarity" about the law on euthanasia.
But she felt that was not being given at a Scotland or a UK-wide level.
'End it all'
Ms McLean said: "We have many situations in which people can choose death with medical assistance, but the one group of people to whom that is not available are those who competently and contemporaneously ask for assistance and I think that is very inconsistent.
"I did a survey in 1996 in which we found that the majority of doctors - we interviewed 1,000 doctors and pharmacists - were actually prepared, in fact enthusiastic, about assisted suicide and euthanasia, and most opinion polls of doctors suggest doctors and nurses are interested at least in the debate coming forward again."
Dr Simpson believed the opinion of doctors was shifting.
"Those of my generation may not be in favour. But I think living wills and the advancement in palliative care and the dealing with suffering in the terminal stages goes a long way to dealing with the problem.
"However, we are left with a small group of people with generative diseases where life and the quality of life is so poor that they wish to end it."
The House of Lords Select Committee is taking evidence on Lord Joffe's Assisted Dying for the Terminally Ill Bill.
It proposes a lifting of the UK ban to "enable a competent adult who is suffering unbearably as a result of a terminal illness to receive medical assistance to die at his own considered and persistent request".
But the Westminster debate will not have a bearing on what happens in Scotland and that is why Jeremy Purvis MSP is proposing a member's bill on the matter.
The Liberal Democrat member for Tweeddale, Ettrick & Lauderdale
said there was considerable public support for a change in the law.
Julia Millington, the political director of the ProLife Party, said the survey should not be interpreted as representing public opinion.
She said: "They have surveyed not 1% or even half a percent but 0.00066% of the population.
"However, the issues at stake here are extremely serious.
"What we haven't been shown are the many patients who are benefiting from first rate palliative care and who completely reject the idea of euthanasia."