Four blasts, claimed by the Taliban, struck the British Council offices in Kabul, while an AFP reporter at the scene reported heavy gunfire ongoing inside the compound.
The British Council is an official organisation part- funded by London which promotes cultural relations in offices around the world.
Police said the first two blasts at least were the work of suicide bombers. Kabul's criminal investigations chief Mohammad Zahir told AFP that at least three people had died but that the casualty toll could rise as attackers are still inside the compound.
"I can confirm that three have been killed so far and there are five or six injured but the casualty toll may rise," Zahir said. He could not confirm whether any of the dead were foreigners.
The British embassy and NATO-led International Security Assistance Force (ISAF) in Afghanistan confirmed that the target was the British Council.
An embassy spokesman said: "I can confirm reports of an attack against the British Council compound in Kabul." He said that the embassy was in contact with Afghan authorities at the scene but could not provide any information on casualties.
The AFP reporter later heard a third, loud explosion followed by a fourth quieter one amid ongoing gunfire.
Taliban spokesman Zabihullah Mujahid, contacted by AFP, claimed that his group was responsible for the attack, which he said was to mark the nation's independence day.