WASHINGTON — An Obama administration program set up to reduce chronic hunger and poverty has contributed to rising incomes for farmers around the world and has helped save millions of people from starvation, according to a report released Monday by the United States Agency for International Development.

The program, Feed the Future, was started by the agency four years ago after a rapid rise in global food prices. It has helped more than seven million small farmers increase crop production and has provided nutritious foods to 12.5 million children in countries hit hard by drought, war or poor development, the report said.

In addition, the United States government received more than $160 million in private-sector investment in 2013 to help farmers and small businesses increase their food production, the agency said, a 40 percent increase from 2012.

The program operates in 19 countries, mostly in Africa, Asia, Latin America and the Caribbean, and has had the greatest success in Senegal, Bangladesh and Honduras, the report found.