It represents a clear increase on an ICM poll carried out for sister paper Scotland on Sunday at the beginning of March, which put the Remain side on 50 per cent of the vote, with 35 per cent backing Leave and 15 per cent don’t knows.
Excluding those who said they are still undecided, the latest poll means that the Remain side now commands a significant majority of 63 per cent, with 37 per cent backing the Leave campaign.
The four-point swing towards Remain over the past two months comes as UK-wide telephone polls suggest it is in the lead, although online polls indicate the two sides are too close to call.
However, the ICM poll also provides further evidence that the EU is far more popular in Scotland than it is elsewhere in the UK. The firm’s most recent Britain-wide poll put the Leave side slightly ahead on 52 per cent, with Remain behind on 48 per cent.
The Scotland Stronger in Europe campaign group described the poll’s results as “encouraging” and evidence that Scots were “bridging other political differences” over the EU referendum issue.
The poll of 1,000 people, carried out earlier this month, shows support for Remain (67 per cent) is strongest among those who voted Labour at last year’s general election, with 22 per cent in favour of Leave and 10 per cent undecided.
SNP voters, however, are more divided on the Europe question, with 51 per cent for staying in, 38 per cent for leaving and 11 per cent undecided.
Those who voted Conservative are more resistant to Brexit, with just 47 per cent believing the UK should stay in the EU, 42 per cent backing Leave and don’t knows accounting for 11 per cent.
The poll also highlights differing levels of support on gender, age and socio-economic lines. While 55 per cent of men believe the UK should remain in Europe and 34 per cent think it should leave, the figures for women are 53 per cent and 29 per cent respectively. However, nearly a fifth (18 per cent) of those women interviewed by ICM said that they are undecided on the issue, compared with one in ten (10 per cent) men.
A significant split exists between younger and middle-aged voters, the poll shows, with 63 per cent of those aged 16 to 24 backing Remain compared to 22 per cent on the side of Brexit and 15 per cent don’t knows.
By contrast, fewer than half (47 per cent) of those aged 45 to 54 believe the UK should stay, with 37 per cent backing Leave and 16 per cent undecided.
A similar divide can be found in socio-economic groups, where 62 per cent of ABC1s intend to vote to stay in the EU, compared with 49 per cent of those in the C2 DE bands.
The poll also shows the strongest support for the Remain camp is in the Lothians (67 per cent) while Central Scotland is home to the strongest support for Leave (39 per cent).
The poll also shows that, over time, more people believe Brexit would have a negative impact on the economy.
On the issue of security in the event of Brexit, 24 per cent said Scotland would be more vulnerable to terrorism if the UK left the EU, a rise of three percentage points on March. However, the same increase was seen among those who said Scotland would be less vulnerable (17 per cent this month; 14 per cent in March).
A spokesman for the Scotland Stronger in Europe campaign said: “These figures are encouraging. They show that people in Scotland have the opportunity to come together on 23 June to vote for Remain, bridging other political differences and potentially having a decisive impact on the result UK-wide. “
No-one from the Vote Leave campaign was available for comment.