Complications of childbirth account for another 720,000 deaths a year, as for the first time neonatal conditions have overtake infectious diseases such as pneumonia as the biggest childhood killer.
Being born too soon, when the lungs, brain and other organs have not developed, can make babies highly vulnerable but the report's authors argue that two thirds of these deaths could be prevented without intensive care
Professor Joy Lawn, of the London School of Hygiene & Tropical Medicine, said: "The success we've seen in the ongoing fight against infectious diseases demonstrates that we can also be successful if we invest in prevention and care for pre-term birth.
"Even very premature babies are surviving in the UK due to improvements in medical care. But babies can spend an average of three months in intensive care. This is traumatic for families and many end up with long-term health complications. It is also hugely expensive for the NHS."
Risk factors for prematurity
Most of the deaths occur in the world's poorest countries, with some of the highest rates in West Africa - where the risk will be even greater now due to Ebola.
The worldwide mortality rate among the under-fives has declined from 76 to 46 deaths per 1,000 live births since 2000. Most of the reduction has been due to progress made in protecting children from diseases like pneumonia, diarrhoea, measles and malaria.
The mortality rate among premature babies has also fallen, but at a far slower rate. As a result, deaths in the first 28 days after birth now make up an increasing proportion of childhood mortality.
"Some 7,600 newborns die daily" said Andres de Francisco, of the Partnership for Maternal, Newborn and Child Health. "We have an epidemic of pre-term and newborn deaths that represents one of the greatest health challenges of the 21st century. "
In the UK pre-term birth complications account for 1,400 child deaths a year - more than double the number in France or Italy. Obesity and later motherhood are among the risk factors for prematurity, as is the rise in the rate of Caesarean deliveries.