She said doctors at local hospital had been "overwhelmed" by casualties and that the death toll could rise.
Dr Muawiyah Hassanein, head of Gaza's emergency medical services, said seven people, all civilians, were killed and 80 people, including several Hamas security personnel, were wounded.
Salam Fayyad, the Palestinian prime minister, said in a statement from his office: "Senior officials in Hamas ordered these crimes which were carried out by the Hamas militia in order to terrify the people ... Now their punishment is a national duty."
Mahmoud Abbas, the leader of Fatah and Palestinian president, on official television denounced "these horrible crimes committed by a band of rebels ... before the eyes of the entire world".
As tensions spilled over between fellow Palestinians in Gaza, Abbas was in the Egyptian capital trying to win more support from Arab neighbours before the planned Annapolis peace conference in the US.
In Cairo, he met Hosni Mubarak, the Egyptian president, and Amr Moussa, the Arab League secretary-general, as well as the visiting foreign policy representative from the European Union.
Abbas then flew on to Turkey where he is scheduled to attend a summit on Tuesday with Recep Tayip Erdogan, the Turkish prime minister.
Fatah officials accused Hamas forces of opening fire from the nearby Islamic University, but Hamas said its men had come under attack from Fatah fighters and fired back.
"Before the rally, Fatah militants were deployed throughout the area," said Ihab al-Ghosein, spokesman for the Hamas-controlled interior ministry.
"Fatah is responsible for continued incitement against the Palestinian police, and there was a clear attempt to bring back chaos."
But Abdullah Abdullah, a senior member of Fatah, told Al Jazeera: "Today is a massacre that is a dark stain on the history of Hamas, the leaders of Hamas and those who executed the attack.
"This was a national event for the Fatah movement," he said, speaking of the rally.
"For Fatah members to come out and remember their leader [Arafat] is not a crime. For the Executive Force, guided by Hamas and ordered by Hamas, to open fire ... is really opening a new page in the civil war in the Gaza Strip and probably beyond."
A Fatah official later said that Hamas security forces had arrested several of its activists, including Mohammad al-Nahal, a senior Fatah political leader in northern Gaza.
Hamas had broken up some smaller demonstrations organised by its rival on Sunday, the third anniversary of Arafat's death.
Speaking at Monday's rally before the gunfire broke out, Odeh called the atmosphere in Gaza City "quite tense".