In the past three days, 21 Palestinians have been killed in fighting in Gaza and two dozen have been wounded.
The latest fighter killed was from the al-Aqsa Martyrs Brigades, a wing of Abbas's Fatah movement. His car was struck by a missile in an Israeli air strike, emergency workers said.
A local commander of the group who was in the car was critically wounded and two passersby were also hurt.
Four Hamas fighters were killed when a house they were hiding in was hit by a series of Israeli missiles, security sources said. A fifth later died of his wounds. Three others were killed in separate raids.
The Israeli military confirmed it had carried out the attacks.
A column of Israeli tanks backed by attack helicopters moved into an area east of the town of Jabalya, outside Gaza City, overnight in part of what Israel has dubbed operation "Rain Man".
Witnesses said that about two dozen tanks moved into the areas of Beit Lahiya and the industrial zone of Beit Hanoun, two northern Gaza towns, after darkness fell on Saturday. A military spokeswoman said the deployment was part of an operation to halt rocket fire at Israel.
Abu Ubaida, a spokesman for Hamas's military wing, issued a statement vowing "we will bombard and strike everywhere" in response to Israel's attacks in Gaza.
He said: "Our reaction will be strong."
Israeli media reported that Amir Peretz, the defence minister, had instructed the military to prevent rocket attacks from Gaza on towns in southern Israel.
The recent fighting comes amid deepening divisions among Palestinians, with forces from Hamas, which controls the Palestinian government, clashing with rivals loyal to Fatah.
At least 250 Palestinians have been killed, around half of them civilians, since Israel stepped up its offensive in Gaza after fighters captured an Israeli soldier in June.
Israel says the offensive is designed to track down the kidnapped soldier and to stop the firing of rockets into Israel. Rocket attacks have increased in recent days.
Three Israelis were wounded by rocket attacks on Friday, a military spokeswoman said.