Mahmoud Abbas, the Palestinian president, has ordered an inquiry into the death.
Palestinian Authority (PA) forces of Abbas have arrested several Hamas members in the West Bank in recent months in their ongoing standoff with the group which controls the Gaza Strip.
Calls for investigation
The Barghouthi clan and resident of Kobar village issued a statement about the imam's death.
The PA was accused of "executing [Barghouthi] without reverting to the justice system and without any justification or right".
The clan then called on "all responsible parties in the committees of the [Palestinian] Legislative [Council] and human rights institutions to work on exposing the truth about what our son, [Majd al-Barghouthi] was subjected to and to try all those responsible for such a crime".
Al Jazeera's correspondent Nour Odeh talked to al-Barghouthi's widow who is convinced that her husband was tortured to death.
Um al-Qassam said: "They killed him on purpose to make an example of him.
"Abbas gives his orders to the security forces to kill any imam or people with specific political affiliations."
The PA intelligence services adamantly denies torturing any of its detainees.
Members of the Palestinian Legislative Council (PLC) announced the formation of a "fact-finding committee" into the incident.
The PLC also said that political detention is illegal "whether in the West Bank or Gaza Strip" and promised to investigate al-Barghouthi's death "in order to prevent further suffering of the people".
The reference was to potential violence that could erupt as a result of the incident.