In a major challenge to the Yes referendum campaign, new figures show 23% of voters believe "Scotland should become independent, separate from the rest of the UK".
The total is the same as the previous low recorded in 2010 and is nine points down on 2011, when 32% backed independence. However, the figures also revealed a stronger appetite for more powers at Holyrood.
The results were based on face-to-face interviews with more than 1200 voters between July and November last year.
They were published by the Scottish Centre for Social Research (ScotCen) in a report co-written by Professor John Curtice of Strathclyde University, the country's leading polling expert.
A further 61% backed devolution; 11% wanted Scotland to remain in the UK without its own parliament, and 5% were undecided.
Asked a differently worded question about where power should lie, 35% of voters said the Scottish Parliament should take "all the decisions for Scotland", down from 43% the previous year.
Nearly six out of 10 voters (59%) said they would be "quite" or "very" worried if Scotland became independent, up from 46% in 2011. Only 21% said they felt confident about the prospect.
There was also a fall in the number of Scots expressing optimism about a range of issues if the country left the UK.
The latest figures showed 42% believed an independent Scotland would have a stronger voice in the world, down from 51% in 2011. The proportion believing independence would instil a greater sense of national pride fell from 67% to 55%.
On the crucial issue of the economy – which ScotCen believes will decide the outcome of the referendum in 2014 – Scots were also slightly more pessimistic overall than the previous year. Thirty-four per cent said independence would improve the economy (unchanged from 2011) while the same number believed it would make it worse (up from 29%). A further 23% said it would make no difference, while 9% were unsure.
As would be expected, support for independence was much stronger among those optimistic about the economic impact. Half of all voters who predicted an improvement in the economy wanted to leave the UK. Among the 6% of voters who said the economy would be "a lot" stronger, support for independence rose to 73%.
The survey shows that the SNP Government's efforts to promote independence since it came to power in 2007 have struggled to translate into support for the policy. Backing averaged 30% from 1999 to 2006, compared with 26% over the course of Alex Salmond's time as First Minister.
While the findings show falling support for independence, they reveal a strong appetite for more devolution.
Nearly two-thirds (64%) said Holyrood should take "most of the important decisions for Scotland" about welfare and benefits, compared with 19% who wanted control to remain at Westminster. More than half (56%) believed Holyrood should take the lead in deciding tax levels.
Mr Curtice said: "During the course of the last 12 months the independence debate moved firmly to the top of the Scottish political agenda. Yet the proponents of independence have
apparently struggled to capitalise on the resulting opportunity to persuade Scots of the merits of their case. Instead, more voters appear to have become concerned about the prospect of leaving the UK."
Scottish Labour's constitutional spokeswoman, Patricia Ferguson MSP, said the survey showed "how out of touch this SNP Government really are".
Scottish Conservative leader Ruth Davidson MSP said the results showed Alex Salmond was "failing spectacularly to sell his dream of separation to the people of Scotland", while for the Scottish Liberal Democrats, leader Willie Rennie said people were "repelled" by plans for independence.
Pointing to an "all-time low" figure of 23% support for independence, Scottish Secretary Michael Moore said it "shows people simply do not believe there are convincing arguments to leave the UK."
A Scottish Government spokeswoman said: "A clear majority think the Scottish Parliament should make most of the important decisions for Scotland, about the level of taxes (56%) and welfare benefits (64%), and over one-third (35%) say Holyrood should make all decisions. An independent Scotland is the only option on offer which meets these aspirations."