The Lloyds TSB Scotland Business Monitor, out today, shows that for the three months up to the end of May 35% of firms said turnover was static and 33% experienced a decrease.
Only 32% of companies showed any signs of increased turnover.
However, the report says that, while there is no sign of a vigorous resurgence in growth, there is a "suggestion of continuing slow recovery" in Scotland at a time when UK-wide figures have shown the double-dip recession is deeper than originally feared.
The Office for National Statistics (ONS) figures, published yesterday, showed the recession, defined as two or more quarters of declining Gross Domestic Product (GDP) in a row, is more severe than first thought.
GDP shrank by 0.4% between October and December, compared with a previous estimate of 0.3%, while the economy contracted by an unchanged 0.3% in the first quarter of this year.
Despite the gloomy picture from the Lloyds Scottish business survey, there are signs of improvement in Scotland, since the net deficit in the figures of minus 1% is an improvement from the minus 6% of the previous quarter.
Donald MacRae, chief economist at Lloyds TSB Scotland, said its survey showed the Scots economy was struggling to maintain a limited degree of momentum.
He said: "However, there is no definite sign of a relapse into a double-dip but a suggestion of continuing slow recovery with low growth.
"Business confidence has not fallen further but remains at a low level.
"A return to more vigorous growth in the Scots economy awaits a rise in confidence in both consumers and businesses. This in turn depends upon convincing evidence of policy initiatives to foster growth in both the eurozone and UK economies."
Labour finance spokesman Ken Macintosh said Finance Secretary John Swinney had "to shoulder the blame for such poor stewardship of our economy".
He said: "He seems more interested in creating further uncertainty over our country's future than restoring confidence by dealing with the pressing issues facing us now."
Tory spokesman Gavin Brown said the Scottish Government action had "to match its rhetoric".
He said: "In particular it should revisit its decision to substantially reduce the housing budget and the college budget as these contribute to economic growth.
"In addition, it should scrap its two new taxes – the retail levy and empty property rates – as these both impact negatively on the economy."
CBI Scotland assistant director David Lonsdale said it was unlikely corporate investment would significantly strengthen without more clarity over the eurozone and public spending.
He said: "However, exports of goods to markets outside the EU have been growing strongly and next year we expect some strengthening in consumption as household incomes begin to rise again. We continue to expect a slow return to health for the economy over the next few years."
A Scottish Government spokeswoman claimed it was doing "all that it can to support the economy" including a £105 million stimulus package announced on Wednesday by Mr Swinney.
She said: "We have already seen positive indicators with the latest labour market statistics, which demonstrate Scotland is outperforming the UK with our employment rate above that of the UK for the 19th consecutive release, and the latest Ernst & Young Attractiveness survey shows that Scotland has the best record of inward investment in terms of job creation in the UK.
"These facts, and comments this week from the Governor of the Bank of England, prove the Westminster Coalition Government's austerity approach is failing."