In the short clips, explosions outside parliament and a central police station are visible, occurring next to passing pedestrians and vehicles.The attacks were conducted by three suicide bombers, police and eyewitnesses said.
The explosions - the first near the central police station and the second very close to parliament - sent bloodied office workers scrambling for cover over shards of broken glass as a plume of white smoke rose above the downtown area.
A single suicide bomber carried out the first blast near the checkpoint at the police station, which killed two people, Enanga said. Then two suicide bombers on motorbikes detonated, killing one other person.
Uganda police spokesperson, Fred Enanga, said "The hallmarks of the attack clearly indicate that the ADF-linked (Allied Democratic Forces) radicalised groups, who still have a desire to carry out lethal attacks on soft targets using suicide attackers and improvised explosive devices."
Over 30 people were being treated at Mulago Hospital, including five people in critical condition, police spokesperson Fred Enanga said.
There was no immediate claim of responsibility.
The al Qaeda-linked Somali insurgent group al Shabaab has carried out deadly attacks in Uganda. Last month another group, the Islamic State-aligned Allied Democratic Forces (ADF), claimed its first attack in Uganda.