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The United States has about 33,600 troops in Afghanistan. It is withdrawing the force in line with Mr Obama's vow to largely end a 12-year mission that began after the attacks in the US on September 11, 2001.
The original plan would see up to 8,000 US troops remain in Afghanistan beyond 2014 for counter-terrorism operations.
Afghan leader Hamid Karzai has agreed to a deal but he refuses to sign a joint security agreement.
Now, Mr Obama has run out of patience, telling Mr Karzai that plans are being drawn up to withdraw all American troops from Afghanistan.
If that occurs, US troops will not be there to train Afghan forces or lead operations against Al Qaeda.
However, the US also has the option to keep a small contingent in Afghanistan next year without Mr Karzai's agreement.
Mr Karzai has already ignored the White House's earlier demand that the deal be signed within weeks, not months.