Spokesman for the provincial governor Attaullah Khogyani has said the fighting has ended and the security forces are now clearing the building.
The four assailants — reportedly dressed as police — fired a rocket propelled grenade from a car outside the British charity’s compound in the eastern city of Jalalabad.
They then clashed with security forces for about three hours, the provincial government spokesman said.
The so-called Islamic State (IS) group later on Wednesday claimed responsibility for the attack.
“A martyrdom-seeking operation with an explosive-laden vehicle and three immersing attacks targeted British and Swedish foundations and Afghan government institutes in the city of Jalalabad,” IS said via its propaganda arm Amaq.