UPDATE 5.05pm: Emerging reports suggest 18 people have been killed and 90 wounded in bombings at the funeral of a protester killed in Kabul.
Earlier: At keast six people have been killed and 90 wounded in bombings at the funeral of a protester killed in Kabul.
A further 87 people are reported to have been injured in the blasts, which come a day after hundreds of demonstrators turned out to demand more security in the capital.
A powerful truck bomb attack in the city three days ago killed 90 people and wounded more than 450.
The attack raised fears about the government's ability to protect its citizens nearly 16 years into a war with insurgents.
Najib Danish, Interior Ministry deputy spokesman, said three explosions rocked a cemetery where Afghan Senator Alam Ezadyar's son was about to be buried.
Salim Ezadyar was one of several people killed during the protest on Friday attended by more than 1,000 people in Kabul.
Alam Ezadyar is deputy speaker for the upper house of the Afghanistan Parliament.
About 200 protesters passed the night under two big tents on a road near the presidential palace and the truck bomb blast site and about 200 more joined them during the day.
All roads toward the palace and nearby diplomatic areas were blocked on Saturday by police and there was limited movement of vehicles and people.
The nature of Friday's demonstration shifted when protesters - many calling for the country's leadership to resign - attempted to move closer to the palace and some rushed police, who fired warning shots and used water cannons and eventually tear gas in attempt to disperse the crowd.
The city's police chief said some demonstrators fired weapons in the direction of his men.
A member of Parliament said on Friday that eight protesters had been shot dead while a hospital official said four corpses were brought to his facility.
On Saturday, General Murad Ali Murad, deputy interior minister, urged demonstrators to disperse because of a high security threat level in the country.
He also called on members of the public not to join the demonstration.
President Ashraf Ghani Ghani, meanwhile, met with senior security officials during an emergency security meeting.
A statement from the president's office said the meeting determined that an investigation must find out what exactly happened that led to the violence and identify those who acted against the law.
Most of the casualties from the truck bombing were civilians, including women and children, officials have said.
The dead also included Afghan security guards at the facilities, including the US Embassy, and 11 American contractors were wounded - none with life-threatening injuries, a US State Department official said.
No one has claimed responsibility for the attack, which came in the first week of the Muslim holy month of Ramadan.