Mahmoud Abbas, the Palestinian president and leader of the Fatah movement, condemned the attack as an act of terrorism.
In a statement he said: "This operation does not go in line with the Palestinian national consensus and the ... interests of the Palestinian people."
However, spokesmen for Hamas, which recently took over the Palestinian government, defended the bombing as a response to what they called Israeli aggression.
Sami Abu Zuhri, Hamas' official spokesman, said the attack was an act of "self-defence" which he said was a reaction to "the continued Israeli crimes against our people".
"The Israeli occupation bears responsibility for the continuation of its aggression. Our people are in a state of self-defence and they have every right to use all means to defend themselves," he said.
Khaled Abu Helal, a Hamas Interior Ministry spokesman, also said the bombing was a legitimate response to Israeli "aggression".
"This operation ... is a direct result of the policy of the occupation and the brutal aggression and siege committed against our people," he said.
Meanwhile, Moussa Abu Marzouk, a Hamas leader in Syria, told Aljazeera that "the Israeli side must feel what the Palestinian feels".
"The Palestinian defends himself as much as he can," he said.