"This important decision paves the way for a sustained presence by NATO allies and partners in Afghanistan. It demonstrates the continued commitment by NATO allies and our partners towards Afghanistan," Stoltenberg said in a statement.
"It's crucial that we continue to support them, practically and financially, to preserve the gains we have achieved in Afghanistan through our joint efforts over many years," he said.
Obama said he would keep US troops in Afghanistan past 2016, when it had been expected that the bulk of its nearly 10,000 soldiers would have been withdrawn.
"Afghan forces are still not as strong as they need to be," Obama said, adding US troops "can make a real difference."
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He said he would keep the 9,800 strong US force in Afghanistan through 2016 and then, rather than be reduced to a normal embassy presence as had been planned, some 5,500 would stay to train Afghan forces and conduct counter-terrorism missions.
The alliance ended combat operations at the end of 2014, leaving in place some 13,000 troops, including the US force, in a training and advisory mission.