"We are seeing lower prices due to abundant supplies, but stronger upturn in demand, such as an increase in the pace of imports from Asia, could limit the decline," said FAO economist Abdolreza Abbassian.
The Food and Agriculture Organisation (FAO) price index measures monthly price changes for a basket of cereals, oilseeds, dairy products, meat and sugar.
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The index, based on prices of a basket of globally traded food commodities, averaged 203.4 points in January, down 1.3% from December and 4.4% below levels in January 2013.
According to the UN body, the biggest fall was in prices of sugar and vegetable oils.
"Sugar and vegetable oils took downward turns of 5.6% and 3.8%, respectively. Meanwhile, bumper cereal crops helped to bring down cereal prices, which were down 1.6% from December and as much as 23% lower than in January 2013," FAO said.
Meat prices, which had strengthened over the past few months, fell slightly in January, it added. The only exception in January was a rise in dairy prices.
"The FAO dairy price index registered a 1.3% increase in January to 267.7 points, largely reflecting strong demand, especially from China, North Africa, the Middle East and the Russian Federation," said Michael Griffin, FAO's dairy and livestock market expert.