The clashes broke out in the southern city of Rafah after thousands of supporters of Fatah, the party of moderate Palestinian president Mahmud Abbas, took to the streets to demand an end to the violence.
The casualties included members of both rival groups.
Witnesses said several hundred armed men were taking part in the demonstration, and that fighting erupted with members of the Hamas-led interior ministry armed forces.
Earlier, in the West Bank, three Palestinians were wounded in similar clashes between Hamas and Fatah, and a waiter in the town of Jericho was pronounced dead after being seriously wounded by gunshots fired by Fatah-linked gunmen.
Government work halted
Meanwhile the Hamas government, which saw its headquarters in the West Bank city of Ramallah stormed by Abbas loyalists on Sunday, has announced that work was being halted in all government ministries.
The government "has announced the suspension of work in government institutions because of the attacks against the seat of government in the West Bank and attempts to kidnap officials," spokesman Ghazi Hamad said.
The Al-Aqsa Martyrs' Brigades called a general strike in protest at Sunday's clashes and it was widely observed in Ramallah, where all the shops in the city centre were closed.
The fresh unrest came as US Secretary of State Condoleezza Rice flew into the Middle East amid pro-Western Arab government warnings that any hope she might have of reviving the peace process would be in vain without an end to the violence.