The wealthiest nations are failing the most disadvantaged of their children, the United Nations reported Wednesday in a study that showed widening disparities even between the middle and lowest household income levels.

The study, published by the United Nations Children’s Fund, or Unicef, focused not on the gap between the richest and poorest segments of societies but rather on the widening disparities between children at the bottom and their peers in the middle.

The purpose of the study, Unicef said in releasing the report, was to “highlight how far children are falling behind in the dimensions of income, education, health and life satisfaction.”

The study analyzed data from 41 countries of the European Union and the Organization for Economic Cooperation and Development. It found that incomes in households below the median had grown more slowly than those above it, “fueling increases in poverty and deprivation among children.”

While inequality gaps in child educational achievement narrowed between those in the lowest and middle groups in these countries, the study found that inequalities in health had widened.

In an overall ranking of the countries, Denmark is the leader, with relatively narrow inequality gaps between children at the low end of income distribution and those in the middle. The overall ranking is weakest for Turkey and Israel, which have the widest inequality gaps.

Disparities in child health, derived from a survey of school-age children that measured the frequency of their health complaints, widened in a majority of the countries, the study showed. The smallest gaps between children at the low end of income levels and those in the middle were found in Austria, Germany and Switzerland, and the largest were in Turkey and Israel.

The study also showed that Canada, France, Iceland and Sweden had fallen in the overall rankings when compared with their performances in recent years. France and Canada, which had been ranked in the middle of the rankings, now are in the bottom third. Iceland and Sweden, which had been toward the top, now are barely above the bottom third.

In the household income category, two of the wealthiest countries — Japan and the United States — were in the bottom third in terms of the relative income gap, which reflects how far the poorest children have fallen behind those in the middle tier. In the United States, the household income disparity between the poorest children and those in the middle is nearly 59 percent, and in Japan it is slightly higher.