The latest Bank of Scotland Report on Jobs also found the number of people placed in permanent posts also continued to grow, although the pace was slower than the record-highs seen in July and August.
Meanwhile, the Bank of Scotland Labour Market Barometer - a composite indicator designed to provide a single figure snapshot of conditions - posted a reading of 60 in September. A figure greater than 50 suggests expansion with last month's number ahead of the 59.7 recorded in August and slightly behind the six-year high of 60.3 seen in July.
The Scottish reading in September was also greater than the 59.2 for the UK as a whole for that month.
Donald MacRae, chief economist at Bank of Scotland, suggested the results indicate the Scottish recovery is becoming more established. Finance minister John Swinney said the figures "signal an improvement in Scottish job market conditions".