Crowds rallied near the site of Wednesday's blast, chanting anti-government and anti-Taliban slogans.
Police in riot gear also used tear gas and water cannon to block them from the presidential palace.
About 90 people died in the bomb blast, one of the deadliest in Kabul in years.
One of those killed during Friday's demonstration was reportedly the son of a prominent politician. Other reports put the death toll at seven, with several other people wounded.