* Retail sales, construction also rebound
* Analysts caution too early to call turning point (Updates throughout)
By George Georgiopoulos
ATHENS, Feb 3 (Reuters) - Greek factory activity grew in January, a survey showed on Monday, marking its first expansion since the country's debt problems came to light in 2009 and plunged the euro zone into a crisis from which it is still recovering.
It is the latest in a series of positive economic data which suggest Greece's six-year economic slump may be bottoming out.
Markit's purchasing managers' index for manufacturing, which accounts for about 10 percent of the Greek economy, rose to 51.2 in January from 49.6 in December, its first time above the 50 line dividing growth from contraction since August 2009.
That came days after data showed Greek retail sales rose in November for the first time since April 2010, while construction activity grew in October for the first time in two years.
Greek stocks welcomed the data with the benchmark share index gaining 2.01 percent to 1,201.88 points.
Still, Greece remains locked in difficult negotiations with its EU and IMF lenders and is expected to require further debt relief and more bailout aid before it can put its debt crisis behind it. Analysts said it was too early to call a turning point.
"Before we go from extreme pessimism to extreme optimism we need to be cautious," said Ilias Lekkos, an economist at Greek lender Piraeus Bank. "Macroeconomic data has started to stabilize and appears slightly improved - but compared to very low levels previously."
Greece's economy has shrunk by a quarter since a recession took hold in 2008 and, in part, deepened due to fiscal rigor demanded by the European Union and International Monetary Fund in return for bailout funds to rescue it from bankruptcy.
Athens and its international lenders expect the 183 billion euro economy to pull out of recession this year, projecting GDP growth of 0.6 percent, while the country's central bank sees it growing by 0.5 percent.
Greece, which has been bailed out twice by the EU and the IMF, has been kept on a drip feed of funds totalling 240 billion euros but they have come at the price of unpopular austerity measures, including tax rises and cuts to pensions and wages.
Unemployment has jumped to record levels - at 27.8 percent it is more than twice the euro zone average - and thousands of businesses have shut.
For manufacturers, a second consecutive rise in incoming new orders in January boosted output levels across the sector, with orders from abroad also strengthening.
"A slight rise in new export orders contributed to the improved performance, though the data inferred that it was the domestic market that provided the principal boost," said Markit economist Phil Smith.
But despite expansions in production and new orders, manufacturers continued to lay off staff in January, with staffing levels having fallen every month since May 2008. (Writing by Karolina Tagaris, editing by Deepa Babington and Toby Chopra)