Over the period July to September, output in the economy increased by 0.7%.
Finance Secretary John Swinney said this showed a "further strengthening in Scotland's economy with the recovery accelerating, even against a backdrop of continuing economic challenges".
The Scottish economy has now been growing for 18 months, with GDP figures for the last six consecutive quarters showing an increase.
But the rise in Scottish GDP for the third quarter of 2013 was slightly less than it was for the UK as a whole, where GDP grew by 0.8% over the period.
The latest figures showed GDP north of the border was 2.1% up on the same period in 2012.
Over the three months from July to September, both the services sector in Scotland - which accounts for almost three-quarters of the economy - and the construction sector north of the border grew by 0.7% while the Scottish production sector expanded by 0.6%.
Liz Cameron, chief executive of Scottish Chambers of Commerce, said the "excellent growth figures" showed that the Scottish economy had increased for the last six consecutive quarters.
She added there was "every possibility" this growth would continue when the figures for the final quarter of last year are published in April.
Ms Cameron said: "The good news is that growth is widely based across a large number of sectors, although much of the growth remains rooted in increasing levels of consumer demand.
"As we enter 2014, we are looking for increased evidence of rising investment to provide a solid basis for continued growth."
Mr Swinney said: "Growth in Scotland's economy has increased and strengthened over the last eighteen months, and this Scottish Government will continue to support growth in key areas to boost Scotland's success.
"It is positive to see that progress has been made in our three major sectors, with construction, production and services industries all posting growth.
"The increase in continued growth in these sectors ensures that we can continue to help build sustainable economic growth for Scotland which will strengthen our economy and create jobs."
He added: "Today's strong growth figures follow recent labour market statistics which show that Scotland is outperforming the UK as a whole on unemployment and employment rates.
"2013 has seen improvements in both output and the labour market. Latest data show that Scotland has a higher employment, lower unemployment and lower inactivity rates than England, Wales or Northern Ireland.
"The emerging picture from recent business surveys also support our confidence in the recovery."
Scottish Secretary Alistair Carmichael said the "positive GDP figures show that Scotland is firmly on the road to recovery as part of the UK".
The UK Government minister added: "Despite uncertain global conditions it is welcome news to see that Scotland's economy has continued to grow into the second half of 2013.
"This Government's long-term economic plan is working and Scotland's economy is successful and stronger as part of the UK with its security, scale and influence.
"The UK's economic growth is now stronger than the main economies in Europe, the deficit is falling and jobs are being created."