Another organization member was severely injured in the incident, the report said.
According to the Palestinians, an Israeli force entered the West Bank city's ancient quarter, and began firing at a group of wanted Palestinians.
Amar al-Anabusi was shot to death and Sufian Kandil, a prominent group member, was severely injured.
The Palestinian sources reported that the soldiers arrived at the area in Palestinian vehicles.
The IDF Spokesperson's Office said that the report was being looked into.