ROME — Global food prices fell slightly in May, but they will remain “at stubbornly high levels” for months to come, a U.N. agency said Tuesday.

The Food and Agriculture Organization said high and volatile prices can be expected into 2012, citing a decline in food stockpiles and modest production increases for most of the crops.

Food prices declined 1 percent in May compared with the previous month, but remain 37 percent above May 2010, according to a price index released by the agency. The FAO said lower cereal and sugar prices led to the decrease in the May index, offsetting increases in meat and dairy prices.

The index hit an all-time high in February, raising fears of a repeat of the food crisis of 2007-2008, when high prices led to violence and political tensions in many parts of the world. Prices in March decreased, though experts warn they remain far too high for many poor communities.

“We have seen month after month of high and volatile food prices and the end is nowhere in sight,” said Luca Chinotti, a policy adviser with the aid agency Oxfam.

In its Food Outlook report, the FAO said the next few months will be crucial in determining how major crops fare this year.

Prospects in major wheat producers Russia and Ukraine are encouraging, the report said, but maize and wheat yields in regions of Europe and North America are in danger because of poor weather.

Northern Europe has been battling a drought that is worrying farmers and threatening to hurt harvests. There also are reports of drought in the southern United States, and too much rain is affecting planting in the northern plains.

“The general situation for agricultural crops and food commodities is tight, with world prices at stubbornly high levels, posing a threat to many low-income food deficit countries,” said David Hallam, director of the FAO’s trade and market division.

The 2011 cereals harvest is projected to hit a record high and register a 3.5 percent increase from last year, FAO said. Starting in July, Russia will lift a ban on grain exports that had been imposed after a severe drought, a move that might help meet increasing demand.