US President Barack Obama promised a decision on post-2014 US troop numbers "fairly shortly," after he flew into the country on a surprise night time visit Sunday.

Obama is deliberating on the size of the force that will be left behind after the longest US war to continue to train Afghan forces, who will shoulder the burden of confronting the Taliban and preventing an Al-Qaeda resurgence.

Obama told the top US General in Afghanistan Joseph Dunford and the US ambassador to Kabul James Cunningham that he was facing tough decisions on the US posture after the end of the year when all combat troops pull out.

He promised an announcement "fairly shortly."

US officials said as Obama flew into Afghanistan aboard Air Force One that they believed that both candidates in Afghanistan's run-off election, Ashraf Ghani and Abdullah Abdullah, would sign a bilateral security agreement that would allow US troops to stay.

But Washington has also warned that without the agreement -- which Afghan President Hamid Karzai has refused to sign -- it may be forced to go to a "zero option" of no troops."

Obama also said that the recent first round of the Afghan election had been a success, and praised the work of building up Afghan forces.

"I will be honest with you, it has gone better than I might have expected a year ago."