The survey found that while 41 per cent back IndyRef2 before 2021, only 22 per cent want a referendum as soon as Brexit takes place.
Overall support for independence is at 44 per cent, while seven per cent were undecided or refused to say. Almost one in five Scots said they wanted another independence referendum regardless of Brexit or its impact.
The results were revealed in an Ipsos Mori poll for STV published this morning.
Almost half (47 per cent) of the 1,050 people who were surveyed were opposed to a potential IndyRef2 and, when asked how they would vote if there was a second referendum, 50 per cent of those likely to take part said they would opt to keep Scotland in the UK.
Support for leaving the UK was highest among those aged 25 to 34, at 59 per cent, but in the over-55 age group 62 per cent said they would vote No.
More than three-fifths (61 per cent) of those surveyed said they believed Brexit would make both Scotland and the UK worse off - but while just nine per cent of SNP supporters and 13 per cent of Labour voters said leaving the EU would boost the UK’s economy, this rose to almost a third 30 per cent for Tory supporters.
The survey, conducted between March 5 and 11, found the SNP is still ahead of its rivals when it comes to Westminster voting intentions - with 39 per cent of those who are likely to vote and who expressed a preference saying they would back Nicola Sturgeon’s party.
Labour was second on 26 per cent, narrowly ahead of the Scottish Conservatives on 25%, while 6% said they would back the Liberal Democrats with four per cent backing other parties.
Emily Gray, managing director of Ipsos Mori Scotland, said: “Scots are pessimistic about the impact that Brexit will have on the economy, both here in Scotland and across the UK. However, Scots’ pessimism about Brexit doesn’t appear to be giving rise to a clamour for a second referendum on Scotland’s constitutional future.
“While 22 per cent of Scots say they support a second referendum in the next three years because of Brexit, there’s still no overall majority in favour of a second independence referendum - our research indicates that opposition to Scotland becoming an independent country remains higher than support for it.
“Meanwhile, the SNP continues to have the highest vote share of any political party in Scotland after almost 11 years in government. While our poll was taken in the same week as Scottish Labour’s spring conference in Dundee, findings do not point to a Scottish Labour ‘bounce’ among voters.”
SNP business convener Derek Mackay said: “People continue to put their trust in the SNP to deliver for Scotland, in the face of chaos from the Tories at Westminster.
“An overwhelming majority are worried about the damage of a hard Brexit to jobs and our economy. And they’re right to be concerned - even the UK Government’s own analysis shows we’re headed for economic disaster unless we protect Scotland’s place in the single market.
“While the Tories think they can do anything they like to Scotland and get away with it, the SNP will continue to stand firm against them.
“That’s why we’re 13 points ahead of rivals at Westminster - the Tories who are responsible for the chaos, and a Labour Party too weak and divided to provide any real opposition.”