Clashes between Fatah and Hamas have left more than 30 Palestinians dead since Mahmoud Abbas, the Palestinian president and leader of Fatah, called last month for early presidential and parliamentary elections.
Hospital officials confirmed that a member of al-Aqsa Martyrs Brigades had been killed by gunfire in the northern Gaza Strip.
Fatah accused the Hamas-led security force of "executing" the man.
A spokesman for the Hamas-led force was not available for comment.
Local residents said members of the Hamas-led force had surrounded the man's home and gunfire ensued. They had sought to question him in response to the roadside bomb.
The bomb blast left a second member of the Hamas-led force in a critical condition and wounded seven others, hospital officials said. Three bystanders, including two children, were among those wounded, they said.
No one claimed responsibility for the bomb attack, which also took place in northern Gaza.
A Hamas spokesman, Abdel-Latif Qanoua, said on Thursday it would "chase those killers who carried out this cowardly action".
Hamas planned to hold a rally in Gaza on Friday to mark the one-year anniversary of its victory over the once-dominant Fatah in Palestinian parliamentary elections.