The police spokesman, who is affiliated with Hamas, Islam Shahawan reported that the explosion occurred when a Jeep carrying six members of a Hamas security force drove over a roadside bomb. After the event, Hamas gunmen started shooting in the air and calling for revenge.
The Hamas-affiliated mosques made announcements condemning the "traitors and Israel's collaborators," an allusion to Fatah members. No organization took responsibility for the event, but Hamas is convinced it was carried out by Fatah.
More than 30 Palestinians have been killed in fighting between rival groups Hamas and Fatah since Palestinian President Mahmoud Abbas called last month for early presidential and parliamentary elections.
Hospital officials confirmed the activist had been killed by gunfire in the northern Gaza Strip.
Fatah accused the Hamas-led security force of "executing" the activist. A spokesman for the Hamas-led force was not available for comment. Local residents said members of the Hamas-led force had surrounded the home of the activist 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 eight others, hospital officials said.
Three bystanders, including two children, were among those wounded, they added. No one claimed responsibility for the bomb attack, which also took place in northern Gaza.
Hamas spokesman Abdel-Latif Qanoua said on Thursday it would "chase those killers who carried out this cowardly action".
Earlier this week, Palestinian factions including Hamas and Fatah resumed talks on forming a coalition government. Similar talks broke down last year.
Hamas has struggled to govern since taking office in March under the weight of US-led sanctions imposed because of its refusal to recognize Israel, renounce violence and abide by interim peace deals. Fatah's Abbas and Hamas leader Khaled Mashaal held inconclusive unity talks in Damascus this week.
The news agencies contributed to this report