Farmers harvest a rice crop in the village of Gangzhong in China's eastern Zhejiang province on November 19, 2013

World food prices fell in January for the first time for three months, because plenty of food is reaching markets and production looks good, the UN's food agency said on Thursday.

But demand, notably in Asia is rising.

A key fell by 1.3 percent from the level in December, the Rome-based Food and Agriculture Organisation (FAO) said.

Its Food Price Index averaged 203.4 points in January as cheaper cereals, sugars, oils and meat outstripped climbing dairy .

"We're 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.

Bumper grain crops helped to bring down cereal prices—down 1.6 percent from December and 23 percent lower than January 2013—and meat prices, which had strengthened over the past few months, also fell in January, the FAO said.

"The only notable exception was a rise in dairy prices... reflecting strong demand, especially from China, North Africa, the Middle East and the Russian Federation," said Michael Griffin, FAO's and livestock market expert.

FAO also released its latest estimate for world cereal production in 2013, forecasting a stronger growth in world cereal production than anticipated—up 8.5 percent from 2012—and said prospects for crops in 2014 were favourable.