Two-fifths of Scots (40%) said they hope Scotland will vote for independence against 47% who want Scotland to remain part of the UK, a poll by Populus for the Financial Times found.
This puts support for independence at 46% once "don't knows" are removed, SNP business convener Derek Mackay said.
Mr MacKay said: "This is a very welcome poll which puts support for becoming an independent country at 46%, excluding 'don't knows'. A Yes vote is well within Scotland's grasp.
"Today and every day between now and September 18, Yes will be speaking to people on doorsteps and high streets about the gains of independence - the momentum is with Yes."
The poll by Populus canvassed 6078 people across Scotland, England and Wales, including 500 in Scotland.
It found the majority of English and Welsh people want Scotland to remain part of the UK: some 55% of those who expressed a strong preference want Scotland to stay while 15% support a split. The other 30% had no strong opinion.
It also found that those south of the border were opposed to a currency union, which has been ruled out by Chancellor George Osborne if Scotland were to become independent.
More than two-thirds (68%) of those polled in England and 59% in Wales were opposed to an independent Scotland continuing to use sterling while retaining the Bank of England as its central bank and lender of last resort.
Many said that an arrangement like that would involve the rest of the UK picking up some of the bill for a bail-out if an independent Scotland were to suffer a financial crisis.
Populus found that about two-thirds of people across all three nations expect the Scots to vote No in the independence referendum which takes place on September 18.
Looking to the future, the poll found that half of Scots thought that in five years time the country would regret a Yes vote.
In England almost eight in 10 (79%) thought Scots would regret splitting from the UK, the Financial Times reported.
Speaking on behalf of Better Together, Edinburgh South Labour MP and shadow business minister Ian Murray said: "It is encouraging that so many people living elsewhere in the UK want to keep our family of nations together.
"This poll also adds to the overwhelming body of evidence that people living elsewhere in the UK do not support a currency union."
A spokesman for Holyrood Finance Secretary John Swinney said: "On currency, another poll conducted in the rest of the UK found that 71% of people supported sharing the pound in a currency union with an independent Scotland.
"However, the question asked here failed to mention any of the mutual benefits of a currency union and was clearly designed to paint a currency union in the most negative light possible.
"Despite this, a clear majority of people in Scotland support keeping the pound as an independent country - which would also give Scotland control of 100% of Scotland's revenues.
"An independent Scotland will keep the pound - and we now know that 'of course' there will be a currency union, thanks to the unnamed UK Government minister recently caught telling the truth."