The president's decisions also allow the military to conduct air support for Afghan operations when needed.
Obama issued the guidelines in recent weeks, the officials said late yesterday, as the American combat mission in Afghanistan draws to a close, thousands of troops return home, and the military prepares for narrower counter-terrorism and training mission for the next two years.
Obama's moves expand on what had been previously planned for next year.
"To the extent that Taliban members directly threaten the United States and coalition forces in Afghanistan or provide direct support to al-Qaida, however, we will take appropriate measures to keep Americans safe," the official said.
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The Taliban's presence in Afghanistan far exceeds that of al-Qaida, adding significance to Obama's authorisation.
The president's authorisation came in response to requests from military commanders who wanted troops to be allowed to continue to battle the Taliban, the US officials said.
The decision to expand the military's authority does not impact the overall number of US troops that will remain in Afghanistan. Earlier this year.
Obama ordered the American force presence to be cut to 9,800 by the end of this year, a figure expected to be cut in half by the end of 2015.
The president wants all US troops to be out of Afghanistan a year later, as his presidency draws to a close.
It took months for the winner of the country's presidential election to be certified, delaying the signing of a bilateral security agreement that was necessary in order to keep US forces in the country after December.