Tawfiq Abu Khoussa, a Fatah spokesman in Gaza, accused Hamas of "shedding Palestinian blood" and said, "Nothing can justify this violence."
A Fatah spokesman in Gaza, Maher Mekdad, said the restructuring was intended to prevent small splinter groups from taking "individual decisions."
Hassan's statement was quickly rebutted by an official Fatah spokesman who portrayed Hassan as endorsing a Hamas coup.
On Saturday, Tawfiq Abu Khoussa, a Fatah spokesman in Gaza, blamed Hamas for starting the latest mayhem.
"There was shooting from the university, and it is a place for weapons storage," said Maher Mikdad, a Fatah spokesman.
Fatah spokesmen say the trucks contained tents and medical equipment, and Hamas has provided no evidence that the trucks were full of weapons.
"Hamas agreed with Abu Mazen before he traveled" to the United States, said Maher Miqdad, a Fatah spokesman in Gaza.
A Fatah spokesman, Abdel Hakim Awad, said Hamas leaders "want to turn Gaza into a new Somalia or Darfur."
"The Islamic University was used as a base for Hamas gunmen," said Maher Makdad, a Fatah spokesman.
He was "executed with 40 gunshots," said a Fatah spokesman, Maher Miqdad.