The order came hours after Hamas declared the ceasefire with Israel dead.
"Ezzedine al-Qassam orders its fighters to avenge quickly and strongly (the death of Ismail Abu Shanab) and to target the Zionist entity.''
"The Zionists have aborted the ceasefire and the answer of Ezzedine al-Qassam is coming," a faxed statement to AFP said on Thursday.
Hamas said it was calling off a three-month truce announced on 29 June in the wake of the deadly air strike here that also killed two others.
"This ugly crime confirms that the Zionists have not respected the ceasefire for one day," the statement said. "They are completely responsible for ending the ceasefire and responsible for what follows."
The unilateral truce came attached with a raft of conditions, including an end to the targeting of militant Palestinians, but the Israeli government never recognised it.
Houses continued to be demolished by Israeli soldiers despite intenrational condemnation.
Hamas vowed revenge shortly after a missile struck Ismail Abu Shanab’s car in Gaza on Thursday, killing him and his two bodyguards.
"The assassination of Abu Shanab is also the assassination of the ceasefire," senior Hamas official Ismail Haniyeh said.
"The Zionist enemy ... fired the last bullet in the suspension of attacks and is completely responsible for all that will follow… We have no choice but to defend ourselves by all means and all possibilities," he added.
Palestine’s other main resistance group, Islamic Jihad, said it will hold a meeting later on Thursday to decide if it will follow Hamas’s lead.
But one of its leaders, Muhammad al-Hindi, said Abu Shanab's death "would make our resistance stronger and strengthen our will to continue."
Palestinian Prime Minister Mahmud Abbas also condemned the assassination as ‘criminal’.
He said the attack will hinder his efforts to rein in resistance fighters.
"We strongly condemn this action because it does not serve peace. Such operations negatively affect all the plans that the Palestinian Authority is undertaking," he said.
However, Gideon Meir, a senior Israeli foreign ministry official, was unrepentant.
He called the Hamas announcement "ridiculous, coming from a movement which claimed responsibility for this horrific attack (in Jerusalem on Tuesday) and attempted a whole string of attacks over the last two weeks."
"The Zionist enemy... is completely responsible for all that will follow… We have no choice but to defend ourselves by all means and all possibilities"
Abu Shanab, a senior Hamas leader, and his two bodyguards were killed in Gaza on Thursday in an Israeli air strike that turned his car into a fireball.
Fourteen people were wounded, four of them seriously, after an Israel F-16 fired volleys of rockets that left Abu Shanab's station wagon a twisted hulk of black, smoking metal.
The body of Abu Shanab was burned almost beyond recognition.
One of the dead bodyguards was identified as Hani Abu El Maren, son-in-law of Hamas spiritual leader Shaikh Ahmad Yassin.
Security sources and eyewitnesses said the F-16 fired three rockets at the car which burst into flames.
When Palestinians rushed to aid the victims, the plane fired two more rockets.
Hundreds of grieving and enraged Palestinians chanting: "Allahu Akbar (God is Great) flocked to the scene of the midday (0900 GMT) attack near the offices of the United Nations.
Hundreds more shouted: "Revenge, revenge", as they milled around the Shafaa hospital where the victims were all taken.
The attack came just hours after the Israeli government authorized reprisals for Tuesday's deadly bombing in Jerusalem that was claimed by Hamas.