Nine people were also wounded in the attack according to Attahullah Khogyani, the provincial governor's spokesman.
No one immediately claimed the attack but the Taliban group and the so-called Islamic State group are active in eastern Afghanistan, especially in Nangarhar.
The two groups have been carrying out near-daily attacks across Afghanistan in recent years, mainly targeting the government and Afghan security forces.
The attacks have continued despite stepped-up US efforts to find a negotiated resolution of the 17-year war.
Mr Khogyani said Wednesday's attack began at 5am, involving five attackers.
Two detonated their explosives, blowing themselves up, while the remaining three were killed in the shooting.
The attackers were on foot and after setting off suicide blasts at the company gates, the others stormed in, triggering a battle that drew US forces to the scene, according to General Ghulam Sanayee Stanikzai, the provincial police chief.
"US forces are supporting Afghan forces in securing the area now," General Stanikzai later said.