Police spokesman Ferdaws Faramarz said the first explosion, which occurred during the rush hour on Tuesday morning, claimed the lives of two people and wounded two others.
He told reporters that the second blast targeted an Afghan Interior Ministry vehicle, leaving two security personnel injured.
A third blast in Kabul caused no casualties.
All the three explosions in Kabul were caused by small magnetic devices known as sticky bombs, according to police.
Taliban denied any involvement in the attacks. The group’s spokesman Zabihullah Mujahid told Reuters that the Kabul blasts “had nothing to do with us.”
Also on Tuesday, a police vehicle was targeted in Parwan Province, north of Kabul. According to police, that attack caused no casualties.
Separately, one soldier was killed and two were wounded in an explosion targeting their vehicle in the eastern city of Jalalabad, Reuters cited Attaullah Khogyani, a spokesman for Nangarhar’s governor, as saying.
The increase in violence in Afghanistan comes even as the government and the Taliban militant group are involved in bilateral talks to end fighting. The two sides reached a preliminary deal last December that sets out rules for further talks. It was the first written agreement between the two sides since the US-led invasion of 2001.