The Israeli military said the air strikes on Thursday were aimed at a cell preparing to carry out an attack. It did not identify the targets. It said two vehicles were fired at, and one was hit.
Pillars of smoke billowed from the destroyed vehicle as burned and dismembered bodies were removed.
Palestinian officials initially said the two men were considered dead and taken to the mortuary by an ambulance. But the doctor at the mortuary found them alive and sent them to the operating room.
A Palestinian health ministry spokesman said they were in critical condition. One lost both legs and suffered severe wounds to his chest, while the other lost a leg and part of his head.
The Islamic Jihad group identified the men as Wael Nassar, 27, and Ahmad Abu Najam, 23 – senior field operatives in its military wing.
Islamic Jihad has called for revenge.
The spokesman for the group, Abu Ahmad, said: “God willing our reprisal is coming and it is going to be like air shaking.
“We are going to shake the air under their feet. They had experienced us in Tel Aviv and more is coming.”
Islamic Jihad, a small group with ties to Iran and Syria, claimed responsibility for last week’s bombing in Tel Aviv that killed nine and wounded dozens.
During more than five years of fighting, Israel has killed dozens of fighters in earmarked air strikes. The attacks also have killed or wounded dozens of civilians.