The explosions were reported near Kampala's parliament and at the central police station.
Three suicide bombers have killed at least three people and set several cars on fire in the centre of Uganda's capital city Kampala.
At least 33 people were hospitalised with injuries sustained in two blasts on Tuesday, police spokesperson Fred Enanga said, and five of the victims are critically injured.
A single suicide bomber carried out the first blast near the checkpoint at the central police station, then two suicide bombers on motorbikes detonated near parliament, Mr. Enanga said.
Parliament had been evacuated, NTV Uganda reported.
Videos posted on social media showed plumes of smoke coming from the city center.
"First responders included Red Cross personnel who were using fire extinguishers to curb the fire on Parliamentary Avenue," the station said on Twitter.
A Ugandan military spokesperson, Brigadier Flavia Byekwaso, said there had been "multiple" blasts and "multiple" casualties but declined to give further details.
Irene Nakasiita, a spokesperson at the Uganda Red Cross, said they would release information about the blasts later.
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, Islamic State made its first claim of responsibility for a blast in Uganda. That bomb — packed with shrapnel — killed a waitress at a restaurant.
Last month another group, the Islamic State-aligned Allied Democratic Forces (ADF), claimed its first attack in Uganda.
Mr. Enanga said he suspected ADF could be responsible for Tuesday's attack.
"Our intelligence also indicates that these are domestic terror groups that are linked to ADF," he said.