The rise followed two months where prices held steady, the FAO said.
There has been concern this year about possible food shortages as drought has hit grain crops in the US Midwest, Europe and central Asia.
The FAO also forecast a decline in global cereal production this year.
It now predicts 2.286 billion tons of cereal to be produced, slightly down from the 2.295 billion tons it estimated a month ago.
The current forecast would mean a 2.6% fall in cereal production from 2011’s record crop.
The FAO said this would result in a significant reduction in world cereal stocks by the end of 2013, but added that very early indications for wheat crops in 2013 were encouraging.
Abdolreza Abbassian, senior economist at the FAO, said that food prices were likely to remain high and volatility could increase.
“Prices are sustained. It is highly unlikely we will see a normalization of prices anytime soon,” he told Reuters.
“Volatility is not going to go away, if anything it may even intensify further in coming months,” he said.
The FAO’s Food Price Index rose 3 points to 216 in September, but this is still well below the record 238 reached in February 2011.
Cereal prices rose 1% from August, as gains in wheat and rice offset a decline in maize.
Meat prices were up 2.1%, with particularly strong gains in the “grain-intensive” pig and poultry sectors.
Dairy prices rose 7%, the sharpest monthly increase since January 2011.
“World demand for milk products remains firm which, combined with increasing feed costs, is underpinning world quotations,” the FAO said.
But sugar prices fell 4.2%, reflecting an improved sugarcane harvest in Brazil, the world’s largest sugar exporter.
Oil prices dipped 0.4%.
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