Bank of Scotland's purchasing managers' index, a composite indicator of economic health, read 51.2 in December.
This was its highest level for six months, although it still indicated just moderate expansion.
It was higher than the 50 points recorded for the UK as a whole, showing that the economy had stalled.
Donald MacRae, chief economist at Bank of Scotland, said "The PMI for December showed a welcome rise to its highest level for six months indicating a return to moderate growth in the Scottish economy.
"These results give hope that the Scottish economy has exited the recent period of slowdown and is entering 2013 in growth mode."
The amount of new business placed with Scottish companies increased for the first time in six months in December, although the report noted that it was "still only modest relative to that registered in the first quarter of 2012".
There are signs of strain as backlogs of work at Scottish businesses have continued to fall.
Output prices have also continued dropping at a time when input prices are rising sharply, suggesting that profit margins are being eroded.
Overall conditions for manufacturers are poor. Factory output in Scotland fell again in December, taking the sequence of decline to six months.
The pace of decline has accelerated slightly since stabilising in October and November.
"Lower demand, leading to a further (albeit slower) decrease in new orders was the primary reason for reduced production levels," Bank of Scotland said in its report.
One positive aspect was that new export orders received by manufacturers rose slightly, having fallen continuously since June.
But this was not enough to protect jobs in the sector, which it had been hoped would lead the country's recovery from the financial crisis.
Manufacturers cut staff for the fifth consecutive month and at a sharper rate than has been seen since August.
The dominant service sector has been having a better time with the level of business activity continuing the growth that it has been experiencing for the past two years.
The employment increase from the sector meant that overall job creation in Scotland was very slightly positive.
A separate study by accountant BDO came to a similar downbeat conclusion.
Its UK-wide study found that business confidence had weakened and that the economy was contracting.
Following a marginal improvement in the fourth quarter of 2012, BDO's output index – which predicts short-run turnover expectations – decreased to 93.1 from a reading of 93.4 last month. Anything below 95 points implies contraction.
This suggests that the UK may experience further contraction in the first quarter of 2013, potentially resulting in a triple-dip recession.
It is widely expected that official figures for the fourth quarter of 2012 will show the UK economy shrank.
BDO partner Peter Hemington said: "Our latest report indicates that many UK businesses are in a state of limbo, as ongoing volatility in the US and eurozone, coupled with sluggish UK GDP (gross domestic product) growth, is leaving them reluctant to hire and make plans for growth.
"Diversifying trade from the unstable eurozone is a must, and it is heartening to see the UK trading more with alternative regions.
"Domestically, the Government must implement measures to expedite growth for UK businesses, especially within the struggling manufacturing sector."