The structure offered plausible deniability to the Fatah leadership, which was careful to distance itself from Black September operations.
The Fatah leadership is dominated by the so-called Tunisians, officials who returned with Mr. Arafat from exile in Tunis in 1994.
Al Aksa is linked to the Fatah movement of the Palestinian leader, Mahmoud Abbas, but it has often been at odds with the Fatah leadership.
The party does not recognize the authority of Mahmoud Abbas and shares Hamas' view that the current Fatah leadership is corrupt and treacherous.
Nonetheless, the Israeli military prevailed and al-Wazir was exiled from Lebanon with the rest of the Fatah leadership.
With his latest move, Mr. Barghouti would be in a position to extract additional promises from the Fatah leadership, and he could still pull out of the election.
Mr. Barghouti's candidacy was hardly more welcome to the Fatah leadership, which has been emphasizing the importance of Palestinian unity.
The Fatah leadership was reported to be having an emergency meeting in Tunis as a result of the reports.
Suddenly, Israel, backed by the United States, found itself propping up the Fatah leadership, in order not to lose the West Bank to Hamas as well.
The gunmen said they were upset with the candidates Mr. Abbas and the Fatah leadership planned to enter in the election.