The UN children's agency UNICEF has warned that its report should serve as a "wake-up call" to the high rate of children in rich countries living in relative poverty.

The report makes clear that "higher incomes do not automatically lead to improved outcomes for all children," said Sarah Cook, director of the UNICEF research center Innocenti. Cook called on all governments to take action in eliminating inequality in child welfare.

Read more: Save the Children charity: 700 million kids 'robbed of childhood'

The report, commissioned as part of the UN's sustainable development goals, examined the well-being of children across 41 countries that generally enjoy high average incomes.

Germany scores well, while child poverty in US above average

The results varied greatly by country. Denmark, Iceland and Norway, where one in 10 children live in poverty, recorded the best results. By comparison, one-third of children live in relative poverty in Israel and Romania.

Overall, the countries that scored best for child well-being were the Nordic countries as well as Germany, Switzerland, South Korea, Slovenia and the Netherlands.

Southern and Eastern European states tended to see the highest rate of child poverty, as well as the Latin American countries.

In the US, meanwhile, 30 percent of children reportedly live in poverty, significantly above the 20 percent global average.

Lack of nutrition, education also widespread

The UNICEF report also looked at various factors contributing to child well-being, including education and food security.

On average, one in eight children face malnutrition in the developed world. However, in the US and UK the rate was as high as one in five; in Mexico and Turkey it was one in three.

Read more: Study finds 2 million poor children in wealthy Germany

UNICEF also warned that even countries with good education systems were at risk. For example, in Finland and Japan, widely believed to have the world's best schooling systems, one-fifth of 15-year-olds don't have the minimum literacy skills.

The report, however, also found a number of positive trends, including drops in teenage pregnancies and youth drunkenness.

dm/cmk (dpa, KPA)