Palestinian Prime Minister Ahmed Qurei vowed revenge in an unusually strong statement.
"No crime goes unpunished," Qurei said of the Israeli attack at a meeting of the Palestinian Cabinet, the Associated Press reported. "For sure there will be retaliation and the retaliation will be justified if it happens."
The attack comes a week after Hamas suicide bombers killed 16 people in simultaneous attacks on two Israeli buses in Beersheba.
Israeli leaders promised to punish Hamas and resume an assassination campaign against Hamas leaders in response to the Beersheba bombings, Reuters reported.
"No one is immune when he carries out terrorist attacks against innocent Israeli civilians," said Israeli Foreign Minister Silvan Shalom.
The attacks on the camp came just after midnight on Tuesday morning as tanks from the Nahal Oz border crossing between Israel and Gaza fired on the town of Shijaia, a Hamas stronghold, while at least five helicopters and warplanes fired missiles overhead, Reuters reported.
The Israeli Army said in a statement that it had "targeted a training field during training of Hamas terrorists." They said that Hamas militants were learning to plant explosives, launch rockets and infiltrate Jewish settlements and posts.
The airstrike produced the highest single-day death toll since May 12, when Israeli troops raided Gaza City and the southern Gaza Strip, killing 15 Palestinians.
Gaza's Shifa Hospital was in a state of chaos and confusion as ambulances and cars brought casualties to the building, the AP reported.
Many Palestinians stood outside the hospital shouting for revenge.
Gaza City remained solemn Tuesday. Children did not go to school, shops closed and students held demonstrations throughout the city, burning tires that produced a plume of black smoke overhead.
Roughly 30,000 people participated in a funeral procession through the city on Tuesday. Militants fired machine guns in the air and the crowd demanded revenge.
"Our response to this crime is coming, God willing, and our twin attack in Beersheba is only one part of many strikes to come," a Hamas militant blared through a loudspeaker mounted on a car.
Tuesday's attack marks the first time the Israeli army has targeted a large group of militants.
Ever since fighting broke out in September 2000, Israeli forces frequently target specific people -- senior militants or activists en route to an attack. Civilians are sometimes killed as well.
Qurei asserted that the attacks hurt peace efforts, saying that they came only a day after Egyptian officials visited the West Bank as part of a mediation effort. Israel has planned to withdraw from Gaza next year and Egypt has stepped in to help secure the area after the pullout.