But the country is largely split on the issue, with widespread concerns about whether terminally ill patients would feel “pressurised” into taking their own lives, according to the poll by ComRes.
The issue is likely to return to prominence later this year when campaigners launch a new drive to push for Assisted Dying in Scotland.
The research commissioned by Care Not Killing - which opposes “physician assisted suicide” - also suggests almost half of Scots fear that it would change their relationship with GPs.
Dr Gordon MacDonald of care Not Killing said: “This poll puts a sword to the lie that changing the law on assisted suicide enjoys unremitting support.
“Abandoning universal protections and expecting doctors to dispense lethal drugs with the express purpose of killing their patients causes alarm. It would undermine the doctor-patient relationship and, as large numbers of the public recognise, risks normalising suicide. ”
Just over half (53%) of Scots said they would trust their own GP to make a decision about their mental capacity to decide whether to seek assistance with dying if they were terminally ill. Less than a quarter (24%) disagreed, while the rest were don’t knows.
Almost half (47%) would be concerned that some terminally ill people may feel pressurised into accepting help to take their own life to avoid being a “burden” to others, the research adds. Almost a third (32%) were not concerned, while the rest didn’t know.
The experience of other countries has also split Scots on the issue. A third of people said it should not be introduced if a rise in “suicides” is seen where it has been in place. A further third disagreed while the rest did not know.
But there was widespread concern among almost half (48%) of Scots that the measure would “fundamentally change” the relationship between a doctor and patient, while 28% disagreed with this. ComRes interviewed 200 Scots between February 8-10 as part of a UK-wide poll of 2040.
Previous polling has suggested that Scots would back the introduction of Assisted Dying and a new campaign to press the case is to be launched by Dignity in Dying in Scotland this year to win over “hearts and minds.”
A spokeswoman said: “The majority of Scots believe that terminally ill, mentally competent adults should be able to access an assisted death at the end of life. Our own figures - in line with three decades’ worth of figures across numerous pollsters - show that 83% of people in Scotland support a safeguarded assisted dying law having been given details of the safeguards involved.”
It has twice been rejected by MSPs at Holyrood in the past decade after legislation was initiated by the late Margo MacDonald. New proposals are unlikely at Holyrood during the current Parliamentary term, but a cross-party group of MSPs has been established to push for change.