Five options were presented, including abolishing the Scottish Parliament, the status quo, increased powers for the Scottish Parliament, independence within the European Union, or independence outside the EU.
Respondents were then asked to rank their preferences, with 34% saying their preferred option would be an independent Scotland in the EU.
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A further 11% named that as their second preference, while 8% backed an independent country outside of the European Union as their first preference with 22% ranking that as their second preference.
Remaining in the UK with no Holyrood parliament garnered 17% of first preference votes, with 22% for the status quo and 19% for remaining in the UK with more devolved powers.
A spokesperson for Progress Scotland said: “This new polling provides a significant insight into the constitutional and political opinions of people in Scotland.
“There should be much for political parties to consider about how their policies and plans reflect the fact that 61 per cent of Scots support some level of greater constitutional change – whether that is regarding Scottish Independence or membership of the European Union.
“The findings of our poll give a fascinating insight into Scottish public attitudes towards support for further devolution to the Scottish Parliament and voters intension in Scotland.”
It comes as a survey for the same organisation published in the Times found Labour falling further behind the SNP ahead of the 2026 Holyrood election.
The polling for the group, which was set up by Angus Robertson, found support for Labour has fallen by four points in Holyrood constituencies and one point on the regional list since September.
Sir John Curtice, the polling expert and Strathclyde University professor, said that would lead to the SNP being the largest party in the Scottish Parliament, but with neither able to form a majority.
The survey had put the SNP on 31% in Holyrood constituencies while Labour had fallen four points to 27%. The Conservatives and Reform UK polled 14% and 10% respectively, with the Lib Dems on 9% and the Scottish Greens on 6%.
Both the SNP and Labour dropped on the regional list, to 27% and 25% respectively, with the Tories and Reform on 15% and 11%, Greens on 10%, Lib Dems on 9% and Alba 3%.
Professor Curtice’s projections put the SNP on 42 MSPs, with Labour on 34, the Conservatives 18, Reform 14, Lib Dems 11 and the Greens 10.
