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Shrapnel from the rocket struck the door of the plane while it was parked on the runway, with two American maintenance crew suffering minor injuries in the attack, Lapan said.
The attack posed no threat to the safety of Dempsey or his staff, who were asleep in their quarters at the time of the incident, officers said.
Although sporadic shelling of Bagram is not uncommon, Taliban insurgents rarely manage to inflict serious damage or casualties at the base, according to military reports.
Dempsey had been visiting Kabul to meet commanders of the NATO-led force and Afghan top brass amid a surge in assaults by Afghan security personnel on their international colleagues.
A total of 10 soldiers, mostly Americans, have lost their lives at the hands of their Afghan allies in the past two weeks, and the attacks have caused almost one in every four coalition deaths in the war so far this month.
The total of 40 deaths so far this year amount to 13 percent of all international coalition fatalities in 2012.
The assaults have confounded the international force, which has touted its partnership with Afghan troops as the key to withdrawing its combat troops over the next two years.
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