One of the shooting victims told The Associated Press that masked gunmen shot him in both legs in the yard outside his Gaza City home in late July, and that it will take him several months to recover from multiple fractures.
The Fatah allegations marked the first concrete sign of a Hamas crackdown on potential domestic dissent during the Israel-Hamas fighting that began July 8.
Hamas spokesman Fawzi Barhoum denied the group put Fatah activists under house arrest as a policy, suggesting some Hamas activists might have acted on their own. Barhoum did not address the shooting allegations.
Hamas and Fatah representatives are also part of a joint Palestinian delegation negotiating the terms of a cease-fire in Egyptian-mediated talks in Cairo.
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Hamas seized Gaza from Abbas in 2007, but in April -- squeezed by a mounting financial crisis -- agreed to hand over some authority in Gaza to an Abbas-led government of experts.
The new government had not yet begun operations when the Gaza war broke out July 8. Hamas remains the sole ruler in Gaza.
Assaf said some of those who Hamas believed had ignored those orders were shot in the legs. He said he did not have an exact number of shooting victims, but said several were being treated in hospitals in the West Bank towns of Ramallah, Nablus and Hebron.
He said they did not want their names released because of fears of Hamas retribution upon their return to Gaza. One wounded Fatah activist, Sami Abu Lasheen, spoke by phone from the Jordanian capital of Amman, where he was undergoing treatment.