"At this moment, we have data about three explosions, there is no confirmed information about the dead or injured. However, they did not affect the desire of citizens to cast their votes," said a police department official.
Pajhwok Afghan News has reported about 15 people killed and more than 110 injured during attacks on polling centers.
Voters were seen fleeing from a school in the north of the Afghan capital after a blast, according to AFP.
An Italian NGO has reported of one baby dying and 29 people being injured. They were among those taken to their hospital after the explosion at a polling station.
People are reportedly continuing to cast their votes amid at least three security incidents around polling stations in Kabul.
According to AFP reports, elections in the two provinces of Kandahar and Ghazni have been postponed as well as in 11 of the country's nearly 400 districts.
Before the vote, members of the radical Taliban* movement, which does not recognize Saturday’s election, threatened civilians and announced their intention of sabotaging the electoral process.
So far, none of the terrorist groups operating in the country has claimed responsibility for the explosions.
Afghans headed to the polls to elect members of the lower house of parliament for the first time since 2010. At least nine candidates have been killed since July 1.
The election was supposed to take place in 2016; however, it had been postponed because of the unstable security situation in the country.
*Taliban is a terrorist group banned in Russia