President Obama has asked the Pentagon to plan for a complete withdrawal of U.S. troops from Afghanistan by the end of the year, but left open the possibility that some troops could remain after 2014.

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President Obama has asked the Pentagon to plan for a complete withdrawal of U.S. troops from Afghanistan by the end of the year, but continues to leave open the possibility that some troops could remain after 2014 -- options he discussed Tuesday with Afghan President Hamid Karzai. 

The two leaders spoke amid an ongoing dispute over a vital security agreement. That agreement would allow the U.S. to keep troops in Afghanistan after 2014, but Karzai is refusing to sign it, saying he wants his successor to sign the pact after elections this spring. 

Obama and Karzai have rarely spoken in recent months, a reflection of the White House's frustration with the Afghan leader. 

The White House has repeatedly said that without a security agreement, the U.S. and international allies will have to withdraw all troops after the war formally concludes at the end of this year. The Pentagon has been pushing for the U.S. to keep up to 10,000 troops in Afghanistan after 2014.