The 70kg device was discovered on the road outside Rashid Abu Shbak's home in the south of the city shortly before he had been due to drive to his office on Sunday.
Abu Shbak, who is one of the most powerful figures in the mainstream, secular Fatah movement of Palestinian president Mahmoud Abbas, was only named to his newly created post of director of internal security last month.
His appointment was hotly contested by the government of the Islamist movement Hamas.
The apparent assassination attempt against Abu Shbak comes just a day after Tareq Abu Rajab, the head of the intelligence services, was seriously wounded and his bodyguard killed in a blast at the services’ headquarters in Gaza City.
A group calling itself al-Qaeda in Palestine said it carried out the botched bombing against Abu Rajab and threatened more attacks, in a statement posted on the internet on Sunday.
"We declare our full responsibility for this operation," the group said in the statement, whose authenticity could not be independently verified.
Sources close to Abu Shbak said the remote-controlled device had been found on the side of the road leading from his home to his office, a distance of less than a kilometre, during a routine sweep.
There was no immediate claim of responsibility by any of the militant factions in the territory, which has become increasingly anarchic since the departure of Israeli soldiers nearly a year ago.
Last week, Palestinian officials said security measures to Abbas had been stepped up amid worries about an assassination plot possibly tied to political rivals Hamas.
Even though Hamas thrashed Fatah in January's parliamentary elections and subsequently formed its first government, responsibility for the security forces remains in the hands of Abbas in his role as president.
Hamas has become increasingly resentful of the conduct of the security forces which are dominated by Fatah followers and have made no progress in tackling the security chaos in Gaza.
Three cars in Aljazeera's car park
in Ramallah were torched
While Abbas was on a tour of Europe last week, Hamas seized the opportunity to roll out thousands of members of a volunteer paramilitary force which had been explicitly vetoed by the president.
Fatah responded by beefing up its own security forces, inevitably raising tensions which have already boiled over into clashes between the two sides.
Hundreds of Fatah supporters staged a demonstration in Gaza on Sunday against the Hamas force which is answerable to the interior minister, Saeed Seyam.
Abbas himself was expected in Gaza on Monday in a bid to defuse the crisis after meeting Israeli ministers at a conference in Egypt.
The Israeli government has no dealings with Hamas - which refuses to renounce violence or recognise Israel's right to exist - but is under pressure not to extend the boycott to Abbas.
Meanwhile, in the West Bank city of Ramallah, scores of Palestinian journalists gathered outside the offices of Aljazeera to protest against the torching of three of the Qatar-based broadcaster's vehicles.
Unknown assailants set fire to a broadcasting van, the bureau chief's car and a third Aljazeera vehicle in an underground car park at the channel's main office in Ramallah late on Saturday, employees and local officials said.
Firefighters took more than three hours to extinguish the blaze, which blackened the building but caused no injuries.
Aljazeera said it had received threats from both Hamas and Fatah before for its reporting.