But Sami Abu Zuhri, a Hamas official, said Israel's actions showed any ceasefire call by Abbas was "worthless".
The armed groups said they would only consider stopping rocket attacks if Israel first called off all of its military operations in Gaza and the occupied West Bank.
Israel has rebuffed similar demands in the past, arguing that its West Bank operations were essential to preventing attacks.
Israel also appeared sceptical about another Gaza ceasefire, arguing it could give Hamas the leeway to increase its hold on power and smuggle in more arms.
Abbas held inconclusive talks with Ismail Haniya, the prime minister from Hamas and other faction leaders, the first such meeting since a surge in factional violence this month verging on civil war.
Despite the latest ceasefire, tensions between Hamas and Fatah remain high. An earlier Abbas-Haniya meeting had been called off after Israel said on Tuesday it could target the Hamas leader if the rocket attacks continued.
In addition to Israel's attack on the car, air strikes just before midnight destroyed two buildings - a flour and oil warehouse and a money-changer's office in the centre of Gaza City - Al Jazeera's Nour Odeh said.
|Israeli ground troops briefly entered a |
south Gaza village on Wednesday [Reuters]
The army said both premises were used to funnel cash for "Hamas terrorism".
An Israeli army spokeswoman said the money-changer had transferred millions of dollars a month from Iran, Syria and Lebanon to Hamas and other groups to buy and manufacture weapons, and to train fighters.
Israeli air strikes over the last eight days have killed at least 35 Palestinians – 23 of them fighters, according to armed groups - while rocket attacks against Israel has killed one woman.
About 50 Palestinians were killed in factional fighting between Hamas and Fatah in the last two weeks although a ceasefire between them seems largely to be holding.