"In addition to the 5,500 US troops that the president has now announced, we anticipate that there will be additional NATO troops remaining in the country in that time period. We are engaged in a process now consulting with our NATO allies and partners about the exact contours of their presence and the numbers," Miller said on Thursday.
Obama announced that Washington will maintain 5,500 troops at a small number of Afghan bases including at Bagram, Jalalabad in the east, and Kandahar in the south after 2016.
The US-led NATO combat force withdrew from Afghanistan in December 2014 after a 14-year occupation. However, over 10,000 US military personnel remain in the country as part of the Resolute Support mission.
The United States planned to end its military presence in Afghanistan by December 2016, closing the remaining bases in the country.
US Defense Secretary Ashton Carter told reporters last week that the United States was considering different options for adjusting its military presence in Afghanistan in 2016 and beyond.
Militant groups such as the Islamic State, the Taliban and al-Qaeda are currently operating in Afghanistan.