A Hamas spokesman accused Israel of violating the Egyptian-mediated truce, which took hold on Wednesday, and said the group would complain to Cairo.
Health officials said Anwar Qdeih, 23, was hit in the head by Israeli gunfire after he approached the security fence that runs between Israel and Gaza – an area that Israel has long declared a no-go zone for Palestinians.
"Anwar was trying to put a Hamas flag on the fence," said Omar Qdeih, a relative who was at the scene.
"The army fired three times into the air. Anwar shouted at them 'Jaabari is behind you', then they shot him in the head," he said.
Israel killed Ahmed al Jaabari, the acting military chief of Hamas' armed wing, on November 14, and launched an offensive in Gaza that aimed to halt Palestinian rocket fire into its territory. In the following eight days of fierce fighting, 163 Palestinians and six Israelis died.
An Israeli military spokeswoman said soldiers fired warning shots into the air to push back some 300 Palestinians who had gathered at different locations along the fence and who were attempting to breach the border.
"After the rioters did not comply, the soldiers responded by firing toward the legs of the rioters," she said.
Hamas spokesman Sami Abu Zuhri said: "We will contact the Egyptian mediator to discuss the incident."
According to the terms of the ceasefire, both Israelis and Palestinians agreed to stop their hostilities. However, the brief document said details on access to the tense border zone would be worked out in the days ahead.
Sixteen Palestinians have been wounded by Israeli gunfire from the border since the start of the ceasefire, health officials said. Fifteen were hurt yesterday and one on Thursday, when the Israeli military said 200 Palestinian "rioters" approached the fence.
Israel's army constantly patrols the border area and says its forces have come under increasing attack this year, with militants planting explosive devices and firing an anti-tank missile on at least one occasion.