Unidentified gunmen fired on the car of Mamoun Swidan, head of Fatah's international relations committee, injuring two of his companions, eyewitnesses told The Anadolu Agency.
Swidan, for his part, survived the attack unscathed, one witness said.
Medical sources told AA that the injuries sustained by Swidan's two companions were "moderate."
Gaza Interior Ministry spokesman Iyad al-Bazam said an investigation had been launched into the incident.
Fatah's West Bank spokesman Ahmed Assaf blamed rival Palestinian faction Hamas for what he described as an "assassination attempt" against a leading Fatah member.
"We hold Hamas leader Khaled Meshaal and his deputy, Ismail Haniyeh, responsible for the terrorism of their armed group in the Gaza Strip and for the attempted assassination of Mamoun Swidan," Fatah said in a statement.
Hamas spokesman Sami Abu Zuhri, for his part, denounced Fatah's accusations.
"The targeting of Fatah leaders in Gaza is a reflection of the internal conflict [within Fatah] between Palestinian Authority President Mahmoud Abbas and Mohamed Dahlan, who was expelled from Fatah in June of 2011," Abu Zuhri told AA.
Abu Zuhri also urged Palestinian security agencies to arrest and prosecute anyone found to be involved in targeting Fatah members.
In April of last year, Fatah and Hamas signed a reconciliation deal that led to the formation of a unity government two months later.
The Ramallah-based unity government, however, has yet to assume full political responsibility for the blockaded Gaza Strip.