The synchronised attacks, calculated to cause maximum casualties, were launched on Sunday in the Kabalagala district, which is frequented by foreign expatriates and aid workers, as well as Ugandans.
The first bomb exploded at 9.30pm, devastating the open-air Telex bar. Plastic tables and chairs were torn apart and one person was impaled by analuminium umbrella pole.
Five minutes later, a second bomb exploded outside a small supermarket next door. Three people were reportedly killed instantly and many others critically injured. Street vendors and passers-by were maimed by flying debris.
The bombings appear to mark a resumption of the violent campaign that rocked the Ugandan capital last year, in which around 26 people died in a series of explosions at bars and restaurants.
The supposedly Islamic fundamentalist Allied Democratic Forces (ADF), a rebel group based in western Uganda, was blamed. If Sunday's bombings are found to be linked to the ADF, it could seriously undermine the government's pretext for invading the Republic of Congo last year. President Yoweri Museveni has consistently claimed his forces are only in the Congo to weed out and crush the ADF rebels.