The percentage of people who intend to vote Yes in the referendum on September 18 has dropped by 2.3 points, a poll by Survation has found.
A second poll conducted at roughly the same time by Panelbase found a 1.2-point decline in support for independence.
The No campaign has also taken a small dent with a drop of 0.35% in both polls. Those who told Survation they don't know how they will vote have risen by 2.5 points while Panelbase saw a rise of one point.
Support for independence, once undecided people are removed, now stands at 44% (-1%) according to Survation and 47% (-0.6%) according to Panelbase.
Support for the UK, minus undecideds, is now 56% (+1%) according to Survation and 53% (+0.4%) according to Panelbase.
Better Together leader Alistair Darling said: "It's increasingly clear that people in Scotland want to have the best of both worlds - a strong Scottish Parliament, with the guarantee of more powers, backed up by the strength, security and stability of being part of the UK.
"While the SNP spend every day talking about how they want to break up the UK, devolution is clearly the settled will of the Scottish people.
"It's no surprise that Scots are rejecting Alex Salmond's negative and divisive campaign when he won't tell us what would replace the pound or how our essential public services, like schools and hospitals, would be funded. Walking away from the UK puts the things we rely on every single day at risk.
"There can be no complacency from those of us who want Scotland to remain in the UK. We will do everything we can to convince those who have yet to make up their mind that we are stronger and better together as part of the UK."
Yes Scotland chief executive Blair Jenkins said: "These are extremely encouraging findings, which show that the referendum is wide open.
"On these new (Panelbase) figures, Yes just needs a three-point swing to move ahead - and we are very confident of achieving success in September. On the average poll of poll figures, the gap between Yes and No has already closed by two-thirds.
"What is particularly significant is that Yes actually has a strong majority if people think that they and their families would be better off in an independent Scotland - and the official figures show that Scotland would be the 14th richest country in terms of economic output per head, compared to the UK's 18th place.
"This confirms our own research that people are attracted to voting Yes - and will choose independence when they are persuaded of the strong economic case for Scotland being in control of our own abundant resources.
"Scotland has got what it takes to be a successful independent country - even our opponents in the No campaign accept that. There is absolutely no doubt that we can be independent - and we are working very hard to win the argument that we should and must vote Yes."
:: Survation sampled 1,002 people aged 16+ in Scotland from April 4-7. Results have been compared with a previous Survation poll between March 6-7.
:: Panelbase sampled 1,024 people aged 16+ in Scotland from April 4-9. Results have been compared with a previous Panelbase poll between March 28 - April 4.