President Ashraf Ghani on Monday called for "serious" investigations into the deaths of four family members killed in Kabul city, the Palace said in statement.
According to the statement, Ghani directed the Ministry of Interior and National Directorate of Security (NDS) to identify the perpetrators and bring them to justice.
Ghani also called for aid to be given to the remaining family members, read the statement.
Three children and a parent were killed by an unidentified man with an axe in Kabul on Sunday evening. The children were between the ages of 7 and 14.
Relatves say they are seeking justice, but have little confidence in the courts or law enforcement.
All were laid to rest in Kabul on Monday.
The relatives said the family had no quarrel with anyone and that the motive behind the killing is so far unknown.
The Interior Ministry has not commented on the incident.
Chief Executive Abdullah Abdullah, who addressed the Council of Ministers meeting on Monday, also insisted on a probe.