The Bank of Scotland's Purchasing Manager's Index recorded a decline in the growth of Scottish economic output in December to a seven-month low and it continues to lag behind that of the UK.
The figures, based on survey data from 600 companies based in Scotland, showed that for the 13th consecutive month companies continued to add workers but also that the rate of employment growth was the slowest since May.
Bank of Scotland chief economist Donald MacRae said: "December's PMI showed the private sector of the Scottish economy continuing to grow although at a reduced rate compared to summer.
"Both service and manufacturing sectors recorded a rise in new work and continued to increase employment in the month."
Scotland's overall PMI reading was 54.5 for December, down from 55.2 in November. This was the third month in a row it has fallen. Anything above 50 denotes growth.
The UK reading slipped to 59.2 from 60.2.
Mr MacRae said this suggests the recovery in the Scottish economy continued at the end of last year "and looks set to persist throughout 2014".
Levels of activity in Scotland's dominant service sector fell to its lowest level since April after slipping for the third consecutive month, on a seasonally adjusted basis.
The manufacturing sector returned to growth in the final month of 2013 after suffering a slight decline in output in November. The Bank of Scotland said the pace of growth in the manufacturing sector was "solid" but still well below highs reached in the middle of last year.
Export orders at manufacturing firms suffered a marked decline in December, the second consecutive month they had declined, highlighting the difficulty that the Government has had in fostering an export-led recovery.
Mr MacRae said this reverse was "perhaps due to a strong pound".
Both sectors have been increasing employment. In the service sector employment growth was "only modest", the Bank of Scotland said, being at the slowest rate since July.
It said that 12% of businesses in the services sector recorded net job creation in December, compared with just under 10% that cut staffing levels.
In the manufacturing sector payroll numbers also grew but at a very muted pace. Some 9.1% of firms reported adding workers while 8.4% cut numbers.
Forecasters are divided over the strength of the economic recovery in Scotland.
In November, the Centre for Economics and Business Research upgraded its growth forecast for 2013 to 1.4% from 0.8% and for the current year to 2.2% from 1.3%.
Strathclyde University's Fraser of Allander Institute expects Scotland's growth rate for 2013 to have amounted to 1.3%. It most recently increased its forecast of expansion in 2014 to 1.8%, from 1.6%. This is below the long-term growth rate of 2%.
The Scottish economy grew by 0.4% in 2012. The Scottish Government viewed the Bank of Scotland numbers as good news.
Cabinet Secretary for Finance John Swinney said: "The PMI figures for December show a positive end to 2013, with private sector output expanding for the 15th consecutive month and employment continuing to rise in both the services and manufacturing sectors.
"We also continued to see growth in new orders in service and manufacturing firms, which should help to get 2014 off to a solid start.
"2013 has seen improvements in both output and the jobs market in Scotland but challenges remain."