The detention center houses about 3,000 prisoners and the majority are already under Afghan control. The United States had not handed over about 100, and some of those under American authority do not have the right to a trial because the U.S. considers them part of an ongoing conflict.
There are also about three dozen non-Afghan detainees, including Pakistanis and other nationals that will remain in American hands. The exact number and nationality of those detainees has never been made public.
A new agreement, or memorandum of understanding, was signed at the ceremony by Dunford and Khan, but the U.S. military said it will not be made public. The agreement supplants one signed last March, which had been made public.
The U.S. military said in a statement that the new agreement "affirms their mutual commitment to the lawful and humane treatment of detainees and their intention to protect the people of Afghanistan and coalition forces," an apparent reference to the release of detainees deemed to be dangerous.
There are about 100,000 coalition troops in Afghanistan, including about 66,000 from the United States. American officials have made no final decision on how many troops might remain in Afghanistan after 2014, although they have said as many as many as 12,000 U.S. and coalition forces could remain.
The U.S. started to hold detainees at Bagram Air Field in early 2002. For several years, prisoners were kept at a former Soviet aircraft machine plant converted into a lockup.
In 2009, the U.S. opened a new detention facility next door. The number of detainees incarcerated at that prison, renamed the Parwan Detention Facility, went from about 1,100 in September 2010 to more than 3,000.
After Monday's handover, it was renamed the Afghan National Detention Facility at Parwan and the U.S. military said it would provide the Afghan army with advisers and $39 million in funding.
The United States has spent about a quarter of a billion dollars to build the Bagram facility along with Kabul's main prison located in the capital.
Patrick Quinn in Kabul and Rahim Faiez in Bagram, Afghanistan contributed to this report.
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