Camp Chapman was the site of one of the worst attacks on the agency in 2009 when a bomber killed seven officials.
No US or coalition soldiers were killed in this latest attack.
The base now houses both Afghan and foreign troops, including US soldiers.
A statement from Khost`s provincial governor said that 27 civilians and six security personnel were killed.
Youqib Khan, the deputy police chief, told the Associated Press news agency that Sunday`s blast hit a checkpoint manned by members of an Afghan unit that guards Camp Chapman.
Officials said those killed were civilians in cars waiting to clear the checkpoint at the time of the blast.
No group has said it carried out the blast, although the Taliban has often targeted troops and launched a fresh offensive in late April.
Khost borders Pakistan and is one of Afghanistan`s most volatile provinces.
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