Only 28 per cent of Iraqi 17-year-olds have sat their final exams, while safe drinking water for children remains scarce, according to the UN.
About 1,350 children were detained by the authorities in 2007, the UN said.
The number of primary school age children not in education in 2006 was 760,000, but this figure has grown over the past year as more displaced children had their schooling disrupted, the UN said.
Despite the urgent needs of Iraqi children, Unicef received only $40 million towards its $144 million appeal for Iraq this year, Veronique Taveau, a Unicef spokeswoman, said in Geneva.
But Unicef said that a recent reduction in violence in Iraq had provided a chance to help Iraqi children, gain access to those in detention, and strengthen government programmes aimed at young people.
It said its funds had enabled Iraqi health workers to conduct house-to-house immunisation of more than four million children against polio and more than three million children against measles, mumps and rubella.
"A new window of opportunity is opening, which should enable us to reach the most vulnerable with expanded, consistent support," Wright said.
"Iraqi children are the foundation for their country's recovery ... We continue to owe them our very best in 2008 and beyond."