The fresh violence is likely to revive fears among Palestinians that Gaza could slip into civil war.
Among the dead were three security officials loyal to Abbas who were killed in the southern town of Khan Younis, hospital officials said.
Abbas's Preventive Security force said the three died when a Hamas police unit ambushed two of its vehicles. Hamas said the security force fired first.
In the Jabalya refugee camp in northern Gaza, one woman was killed after getting caught in the crossfire between rival forces.
That clash came after unknown assailants killed a Fatah member who was on a rooftop in the town of Beit Lahiya and a car carrying Hamas security officers was ambushed. Two policemen were wounded in the ambush, the Hamas police force said.
|"We believe his life is at serious risk and we urge his captors to release him immediately"|
Sakher Abu El-Awn, Gaza office manager of the French news agency Agence France-Presse
Armed men also abducted four Fatah members from the streets, witnesses said. Fatah blamed Hamas, which declined to comment.
While Abbas has called for fresh parliamentary and presidential elections, he has left the door open to talks with Hamas on forging a unity government that Palestinians hope will lead to the lifting of Western sanctions imposed on the Hamas administration.
On top of the internal chaos, general law and order has deteriorated in Gaza in recent months.
Meanwhile, Palestinian colleagues of a Peruvian photographer abducted by armed men this week demanded his release on Wednesday, saying the 50-year-old's life was in danger because he needed medicine for heart disease.
Sakher Abu El-Awn, Gaza office manager of the French news agency Agence France-Presse, said Jaime Razuri, who was seized outside the AFP Gaza City office on Monday, was taking several types of medication, including some for the heart problems.
"We believe his life is at serious risk and we urge his captors to release him immediately," Abu El-Awn told Reuters.
Nour Odeh, Al Jazeera's correspondent in Gaza, reports that despite the violence, both parties are saying the ceasefire still holds.
She also said: "These kinds of clashes are looked down upon by ordinary Palestinians."