* FAO food price index falls 2 points to 209
* Food index averages 212 in 2012, down 7 pct
* Prices to stay high but situation may be calmer (Adds economist quotes, details, background)
By Catherine Hornby
ROME, Jan 10 (Reuters) - Food prices will stay at high levels in 2013 and low stocks pose the risk of sharp price increases if crops fail, the United Nations' food agency said on Thursday, after its index showed prices fell for the third month running in December.
A surge in food prices over the summer of 2012 fuelled by the worst drought in more than half a century in the United States and dry weather in other major exporters raised fears of a new food crisis such as the one seen in 2008.
But the Food and Agriculture Organisation's (FAO) Food Price Index, which measures monthly price changes for a basket of cereals, oilseeds, dairy, meat and sugar, fell for the third month in a row in December to 209, its lowest level since June, led by declines in cereals and oils prices.
Soy prices have fallen on forecasts of near-record South American production, bringing down other grains prices.
For 2012 as a whole, the index averaged 212, down 7 percent compared to 2011, but still at historically high levels.
"Prices are high and will remain high in 2013/2014," FAO senior economist Abdolreza Abbassian said in a telephone interview.
"The fact that stocks remain low and the possibility of hopefully a better economic situation in 2013/14 that should encourage consumption are issues the market will get some price support from," he said.
FAO said in December it expected world cereal stocks to be about 495 million tonnes at end-2013, down 5 percent from their opening level.
Nevertheless Abbassian said that better international coordination was helping prevent countries from using export bans, which was creating a calmer situation compared to 2008, when unexpected national controls worsened the food crisis.
Good supply prospects for corn and soybeans in the southern hemisphere would help offset tightness in the northern hemisphere, reducing the risk of supply shocks, he said.
But the situation for wheat remained more cautious, he said, due to concerns over high usage and a lack of high quality wheat in the market.
FAO's index is below a peak of 238 points hit in February 2011, when high food prices helped drive the Arab Spring uprisings in the Middle East and North Africa.
In the summer of 2012 it reached levels close to those seen in 2008 when riots, some deadly, broke out in several poor countries. (Editing by Keiron Henderson)