Two civilians and a policeman were killed in the blasts, police spokesman Fred Enanga told reporters at a press conference in the town.
ISIS-affiliated Amaq news agency reported the incident on its Telegram channel on Tuesday, saying three fighters left with bags full of explosives. Two made their way to Kampala central police station and the third to the parliament building, where they exploded, he reported.
Police said the attacks bore the hallmarks of the Allied Democratic Forces (ADF), an Islamist rebel group affiliated with ISIS.
In a statement released on Tuesday, Ugandan President Yoweri Museveni raised the number of people injured from 33 to 36. He said three attackers died while detonating their bombs and seven were killed while resisting arrest. A total of 81 suspects have been arrested, Museveni said.
“Therefore, the public must remain vigilant and control people at the entry points of bus parks, hotels, churches, mosques, markets,” he added.
The two explosions rocked the city center within five minutes of each other. Police said surveillance footage showed an adult male carrying a backpack blowing himself up at 10:03 a.m. local time near the central police station. Enanga said the attacker died instantly.
Two people were confirmed dead at the scene of the first explosion, while 17 others were seriously injured, Enanga said in a statement.
Three minutes after the first explosion, two motorcycle suicide bombers were seen exploding near Raja Chambers and the Jubilee Insurance Building, along the central avenue of Parliament in Kampala, Enanga said. Both bombers died and the body of a civilian was also found at the site, he added.
Enanga said 33 people were injured in the two blasts; five of them are in critical condition. The injured are treated at the national referral hospital in Mulago.
Police pursued a fourth suicide bomber, Enanga said, adding that two more bombs had been recovered from his home and would detonate safely.
In the aftermath of the bombings, police and military cordoned off the streets around the blast sites and restricted traffic in the city.
Last month, an explosion in Kampala killed at least one person and injured several others. Reuters reported that Islamic State claimed responsibility for the explosion.