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.
A Ugandan military spokesperson told Reuters that there had been "multiple" blasts and "multiple" casualties but declined to give further details.
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.