Previously, the president had said US-led NATO combat operations would finish at the end of this year.
The NATO follow up mission, to take over on January 1 with 9,800 US troops and about 3,000 soldiers from Germany, Italy and other member nations, was to focus on supporting Afghan forces as they take on the Taliban, in parallel with US counter-terrorism operations.
But in a strategic shift, the New York Times said, Obama signed an order authorising US troops through 2015 to carry out missions against militant groups, including the Taliban, that threaten them or the Afghan government.
The new order also allows for air support – from US jets, bombers and drones – for Afghan combat missions.
The newspaper said civilian advisers argued against the broader mission for 2015, objecting to putting American lives in danger in the fight against the Taliban and recommending a narrower, counter-terrorism focus against Al-Qaeda.
“There was a school of thought that wanted the mission to be very limited, focused solely on Al-Qaeda,” one American official told the paper.
But, the official said, “the military pretty much got what it wanted.”
However, a senior official told the Times that US forces next year would not carry out regular patrols against the Taliban.
“We will no longer target belligerents solely because they are members of the Taliban,” the official said.
“To the extent that Taliban members directly threaten the United States and coalition forces in Afghanistan or provide direct support to Al-Qaeda, however, we will take appropriate measures to keep Americans safe.”
The newspaper said the change was in part related to the rapid advance of jihadist Islamic State militants in Iraq, which has sparked criticism that Obama pulled troops out without a fully-prepared Iraqi military in place.
It also said that new Afghan president Ashraf Ghani was more open to accepting a wide-ranging US military mission than his predecessor Hamid Karzai.
Earlier this month, US defence officials had said commanders were weighing a delay in withdrawing American troops from Afghanistan after the country’s protracted election set back preparations for the transition.
At its peak, the US force rose to more than 100,000 in Afghanistan, and there are now 27,000 troops deployed.