Under initial plans, US troop numbers were to be reduced to 5,500, from a current level of 9,800.
The US ended major combat operations in Afghanistan at the end of 2014.
The mission of the remaining US troops is to train Afghan forces and support operations against al-Qaeda and other militant groups.
Mr Obama told reporters that the security situation in Afghanistan remained "precarious", with the Taliban still mounting suicide attacks in the capital Kabul and other cities.
