President Barack Obama approved the move despite an earlier plan to limit the US force to a maximum of 9,800 troops in 2015.
A protracted Afghan election delayed the signing of security deals with the United States and NATO countries, which set back plans for Western governments to contribute troops to the post-2014 mission, named "Operation Resolute Support", Hagel said.
Due to "delays in signing these agreements, the force generation effort for (Operation) Resolute Support is several months behind where we hoped it would be at this time", Hagel told reporters.
"This will mean the delayed withdrawal of up to 1,000 US troops -- so that up to 10,800 troops, rather than 9,800, could remain in Afghanistan through the end of this year, and for the first few months in 2015."
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Hagel said Obama's decision did not change the mission for the troops next year -- which will focus on training Afghan forces -- nor did it alter a long-term deadline for a US troop drawdown over the next two years.
Washington was "committed to preventing Al-Qaeda from using Afghanistan as a safe haven to threaten the United States," he said.