Baha Khatari was a member of the Abu Ali Mustapha Brigades, the military wing of the Popular Front for the Liberation of Palestine, Palestinian medical and security sources said.
An Israeli military spokeswoman said soldiers had come under fire during a raid in the camp during which explosive devices were thrown at them. She said the unit reported firing at two fighters and hitting one of them.
Sixteen Palestinians suspected of "terrorist activity" had been arrested overnight in the West Bank, she added.
Meanwhile, the Israeli army has denied accusations from human rights campaigners that it shot dead two unarmed Palestinians as they lay wounded in the West Bank on Wednesday.
The B'Tselem rights group said it had "grave concerns" that the two men were not killed outright along with three other suspected Palestinian fighters - as initially reported by the army - but as they lay wounded.
Salim Abu al-Haija and Mahmud Abu Hassan were killed following a raid in the village of Yamun near Jenin.
"The testimonies [of witnesses] raise a grave concern that Salim Abu al-Haija and Mahmud Abu Hassan were executed by the soldiers, while they were unarmed, wounded, and posed no risk to the soldiers."
B'Tselem, an Israeli human rights organisation
B'Tselem said that according to witnesses the two men managed to escape the initial encounter and took refuge in a nearby house.
Witnesses "saw soldiers enter a side room, where Abu al-Haija was lying and after a minute or two, heard gunfire. Then, two of the witnesses saw one of the soldiers fire at Abu Hassan."
"The testimonies raise a grave concern that Salim Abu al-Haija and Mahmud Abu Hassan were executed by the soldiers, while they were unarmed, wounded, and posed no risk to the soldiers," it said.
On Tuesday, the army said that "following the exchanges of fire, the force called residents of a structure, in which additional armed gunmen were suspected of staying, to leave it."
The Israeli unit then entered the building "only after the commander of the ... force made sure, by asking the local Palestinians, that there were no other people inside it."
"During the searching, the force identified several suspicious figures inside the structure and fired at them," it said.
"It is important to stress that the local Palestinians who were asked by the force whether all of the structure's resident have left it, not only concealed the fact that the gunmen were inside, but told the force that the structure was totally vacant," it said.
B'Tselem called for the military police to immediately open an investigation into the incident.