The survey by YouGov found 46 per cent of respondents north of the Border want an IndyRef2, without specifying a date, with 43 per cent against and 11 per cent undecided.
But the poll found 48 per cent of respondents from across the UK as a whole were against the idea, with 27 per cent in favour and a quarter undecided.
The prospect of a further vote on independence has been brought back into sharp focus following last week's general election result, which saw the SNP win 47 of 59 seats in Scotland but the Tories returned to power with an overall majority in the Commons.
But the UK Government has consistently said it will not grant Holyrood the legal powers required for a further referendum, with Boris Johnson telling Nicola Sturgeon when the two leaders spoke on the phone recently that the 2014 result must be respected.
The Nationalists’ depute leader, Keith Brown, said: “The SNP has a clear, explicit and repeated mandate to deliver an independence referendum – and it would be entirely undemocratic for any politician to stand in the way.
“Scotland’s future must be in Scotland’s hands – not Boris Johnson’s."
Yesterday, Nicola Sturgeon told MSPs there needed to be co-operation to "protect Scotland" from the risks of a "Brexit-focused Tory government", and claimed the election result had given the SNP a mandate to ask for a second independence referendum.
But Pamela Nash, chief executive of Scotland in Union, said: “Nicola Sturgeon is trying to sound reasonable, but what she is saying is anything but. The General Election result did not provide her with a mandate for a divisive and unwanted second independence referendum.”