Almost all the world's undernourished live in developing countries, where food prices have fallen more slowly than in the richer nations, the report said. Poor countries need more aid and agricultural investment to cope, it said.
"The silent hunger crisis, affecting one-sixth of all of humanity, poses a serious risk for world peace and security," said the agency's Director-General Jacques Diouf.
Soaring prices for staples, such as rice, triggered riots in the developing world last year.
Hunger increased despite strong 2009 cereal production, and a mild retreat in food prices from the highs of mid-2008. However, average prices at the end of last year were still 24 percent higher in real terms than in 2006, FAO said.
The global economic crisis has compounded the problem for people dealing with pay cuts or job losses. Individual countries have also some lost flexibility in handling price fluctuations, as the crisis has made tools such as currency devaluation less effective.
The report predicted the urban poor would likely be hit hardest as foreign investment declines and demand for exports drops, and that millions would return to the countryside, which in turn could put pressure on rural communities and resources.
Globally there are now about 1.02 billion people hungry, up 11 percent from last year's 915 million, the agency said. It based its estimate on analysis by the U.S. Department of Agriculture.
Asia and the Pacific, the world's most populous region, has the largest number of hungry people at 642 million.
Sub-Saharan Africa has the highest hunger rate, with 265 million undernourished representing 32 percent of the region's population.
In the developed world, undernourishment is a growing concern, with 15 million now hungry, the report said.
The crisis also affects the quality of nutrition, as families tend to buy cheaper foods, such as grains, which are rich in calories but contain fewer proteins than meat or dairy products.
Diouf urged governments to immediately set up social protection programs to improve food access for those in need. He said small farmers should be helped with seeds, tools and fertilizers.
He urged structural, long-term changes, such as increasing production in low-income countries, noting that world hunger had been increasing before the financial downturn.
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