At least eight civilians were killed after 23 rocket-propelled mortars landed in at least six police districts of the Kabul on Saturday, the Interior Ministry said.
A further 31 people were wounded, the ministry said.
The mortars were shelled from two mini-trucks which were parked in police district 17 and 4, according to the Ministry.
The ministry said the number of casualties would be updated later in the day.
Among the targets was the famous Sedarat square, where the office of Afghan Vice President Amrullah Saleh is located.
No group has claimed responsibility. The Taliban denied involvement.
An hour after the attacks, Saleh said on Facebook that his morning meetings for securing Kabul had not reached the desired goals, but did not give further details.
Footage of the attacks that went viral on social media showed some rockets landing in civilian-populated areas.
US ambassador to Kabul Ross Willson said that Afghans should not live in terror, and that his country would “work with Afghan partners to prevent such attacks and hold their perpetrators to account.”
The UN mission in Afghanistan (UNAMA) said in a tweet that the agency was deeply shocked by the attacks on civilians, and added that “those responsible must face justice.”
The attacks come two days after a visit by the Pakistani prime minister during which he promised that his government would do what was necessary to reduce violence in Afghanistan.
The government of Afghanistan has always blamed Pakistan for the ongoing conflict in Afghanistan by employing proxy forces such as the Taliban and Islamic State militants. Pakistan denies the claims.