The explosions, carried out by Taliban suicide bombers, occurred in the Karte Parwan area of the city, near the Intercontinental Hotel and the residence of First Vice President Mohammad Qasim Fahim.
The explosions struck at the British Council offices and witnesses reported that heavy gunfire was ongoing inside the compound.
Earlier it had been reported that the explosions happened at or near the Indian Cultural Centre. However, a Ministry of External Affairs official in New Delhi told rediff.com that its building had not been targeted.
Two explosions were reported within about 10 minutes of each other around 5:45 am (local time).
Military helicopters buzzed over the area as police cordoned off the scene.
The British Council is an official organisation part-funded by London that promotes cultural relations in offices around the world.
Friday is a national holiday in Afghanistan, marking the country's independence from Great Britain in 1919.
Photo Courtesy: Twitter
PHOTO Album: The long war in Afghanistan
Ministry to address Boxing Federation's grouses
Mohammad Yousuf retires from all forms of cricket
US swimmer forced to end Cuba-Florida swim: CNN
Great places in Mumbai to feast at this Ramadan