Nearly 3000 civilians were killed and more than 5600 were injured.
The UN report said the gradual withdrawal of foreign troops left Afghan government forces more vulnerable to attack by insurgents.
The UN Assistance Mission for Afghanistan said 34% more children and 36% more women were killed and wounded in 2013 than in 2012.
The spike in casualties reverses a fall in 2012. The deadliest year of the war was 2011.