Witnesses and local sources told Aljazeera the street battles on Monday night near the al-Saraya security headquarters were related to previous disagreements between elements of the Palestinian Authority's internal security service and military intelligence agents.
The identities of the casualties were not immediately clear. Neither side has commented.
The Palestinian security apparatus has been hobbled by corruption charges and factional feuds as well as Israeli attacks on its infrastructure.
The appointment of Musa Arafat, a cousin of Yasir Arafat, as chief of military intelligence in July drew violent street protests from Gaza activists who demanded reform in the Palestinian old guard.
On 12 October, Musa Arafat survived a car bombing against his convoy that he blamed on Palestinian enemies.
One group, the Popular Resistance Committees, accused him of trying to kill its leader.
The deteriorating situation has posed one of the greatest internal challenges to Yasir Arafat since he returned from exile.
It has also raised the spectre of chaos in Gaza once Israeli troops and settlers withdraw next year under a plan by Prime Minister Ariel Sharon.