NTV Uganda said "scores" had been injured and there had been two blasts - one very close to parliament and one near the central police station. Parliament was being evacuated, the television station reported.
An NTV Uganda reporter said he saw two bodies. The cause of the blasts was not immediately clear.
"First responders included Red Cross personnel who were using fire extinguishers to curb the fire on Parliamentary Avenue," the station said on Twitter, Reuters reported.
A Ugandan military spokesperson, Brigadier Flavia Byekwaso, told Reuters that there had been "multiple" blasts and "multiple" casualties but declined to give further details.
Irene Nakasiita, spokesperson at the Uganda Red Cross, said they would release information about the blasts later. The spokesperson for Uganda's police did not respond immediately to requests for comment.
Ugandan soldiers are fighting al-Qaeda-linked al-Shabaab insurgents in Somalia as part of an African Union peacekeeping force. Al-Shabaab has carried out several deadly bombings in Uganda.
Last month, Daesh (ISIL or ISIS) made its first claim of responsibility for a blast in Uganda. That bomb - packed with shrapnel - killed a waitress at a restaurant.
Also last month, Ugandan police said a suicide bomber had exploded on a bus, killing himself and injuring others.