British Prime Minister David Cameron said he spoke with New Zealand Prime Minister John Key and thanked him for the troops' role in ending the raid, in which 10 people were thought to have been killed.
"It's obviously a tragic but cowardly act that has been undertaken but it won't succeed and it won't deflect us from the vital work we are doing in Afghanistan," Mr Cameron said.
The attack started with one suicide bomber detonating an explosives-laden car outside the British Council while another suicide bomber struck inside the compound, according to Afghan police.
Afghan security forces dispatched to the scene said that at least three insurgents fought from a secure bunker inside the compound with rifles and rocket propelled grenades.
An Afghan policeman named Azizullah said that the insurgents wrestled weapons and ammunition from the guards at the compound.
The dead included eight Afghan policemen, a security guard whose nationality was not immediately known and an Afghan municipal worker, according to Kabul police official Farooq Asas.
Two of four people wounded in the blasts were not Afghans, he said.
The British Council is an official organisation part-funded by the British government that promotes cultural relations in offices around the world.
- NZPA
