The announcement came shortly after ISIS attacked a television channel in Kabul killing two people.
Speaking at a news conference in Brussels, NATO secretary-general Jens Stoltenberg said the deployment was meant "to help the Afghans break the stalemate" with militants.
The US also recently announced an additional troop deployment to Afghanistan.
Why is NATO deploying additional troops to Afghanistan?
What is NATO?
The North Atlantic Treaty Organization (NATO) is based on the North Atlantic Treaty signed on 4th April 1949 between the US and its allies. Article 5 of the treaty obligates them to collectively defend an alliance member threatened by external aggression.
NATO in Afghanistan
NATO intervened in Afghanistan in 2003 when it took command of the UN-mandated International Security Assistance Force (ISAF).
This was to encourage the Afghan officials to provide efficient security to their country from terrorism and equip them to defend themselves.
It continues to maintain a presence in Afghanistan through Operation Resolute Support, a follow-up to ISAF which was disbanded in 2014.
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What did Stoltenberg say?
Stoltenberg condemned the attacks on Shamshad TV and revealed that NATO would increase its troop presence in Afghanistan from 13,000 to 16,000.
He stressed that the additional troops would be employed for assistance and training rather than combat duties.
He also conveyed that NATO was raising the issue of Pakistan's terrorist safe-havens.
"No country should provide havens to insurgents," he added.
The US is also increasing its troop deployment
President Donald Trump earlier favored US withdrawal from Afghanistan but was forced to reconsider due to its deteriorating security situation.
In February, Gen. John Nicholson, a US commander of the NATO mission, said additional troops would help weaken the Taliban and other extremist groups.
In September, US Defense Secretary Jim Mattis announced that Washington plans on deploying 3,000-5,000 additional troops to Afghanistan.