The assessment looks at progress towards achieving the fourth Millennium Development Goal (MDG), which calls for a two-thirds reduction in the mortality of children aged less than five in 2015 compared to 1990.
As of 2007, there had been a fall of 52 percent in the UN's East Asia and Pacific region, and declines of 53 percent in Latin America and the Caribbean, Central and Eastern Europe and the former Soviet republics of Central Asia.
In sub-Saharan Africa, the fall was 21 percent, ranging from a high of 26 percent in the east and south of the continent to just 18 percent in Western and Central Africa.
In absolute numbers, the global number of deaths of under-fives has fallen from 12.8 million in 1990 to 9.2 million in 2007. There was a fall of 200,000 in 2007 over 2006 alone.
The mortality rate among rich countries in 2007 was six deaths for every 1,000 live births, compared with 68 deaths for the world as a whole, but 147 in sub-Saharan Africa and 78 in South Asia.
"Substantial progress has been made towards the achievement of MDG 4," although in much of sub-Saharan Africa and South Asia, "progress is still grossly insufficient," says the paper by the UN Children's Fund.
The paper is published to mark the 30th anniversary of the so-called Alma-Ata Declaration, considered a landmark commitment to tackling infant deaths.