Director-General Jose Graziano da Silva says the latest data is "reassuring." Agency officials say the food price index of basic foods remained unchanged in August from July.
FAO official David Hallam told reporters in Rome on Thursday that "there is no strong evidence" to suggest another food price crisis, such as that which sparked unrest in the developing world in 2007-2008.
FAO's latest monthly report found that while there was no overall rise in food prices last month, prices are still high.
While meat and dairy prices rose, sugar prices fell sharply. July's index had reflected soaring prices amid droughts affecting corn and wheat crops.