The United Nations on Tuesday reported significant declines in the rates of child mortality and hunger, but said those two scourges of the developing world stubbornly persist in parts of Africa and South Asia despite major health care advances and sharply higher global food production.

The trends, detailed in two annual reports by United Nations agencies, were presented before the General Assembly meetings of world leaders, where the Millennium Development Goals, a United Nations list of aspirations to meet the needs of the world’s poorest, are an important discussion theme.

While one of those goals — halving the number of hungry people by 2015 — seems within reach, the goal of reducing child mortality by two-thirds is years behind, the reports showed.

The child mortality report, a collaboration of Unicef, other United Nations agencies and the World Bank, showed that the mortality rate for children younger than 5, the most vulnerable age group, had dropped by nearly half between 1990 and 2013. Nearly all of the countries with the highest mortality rates are in Africa, the report said, and two countries that are among the world’s most populous — India and Nigeria — account for nearly one-third of all deaths among children younger than 5.