Saturday's incident took place east of Khan Yunis, a city in the southern Gaza Strip, and according to the military, the suspects were placing an explosive device along the border when they caught the soldiers attention.
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In Gaza, sources reported that one of the Palestinians, in his twenties, was injured by Israeli fire.
Ashraf al-Qudra, a spokesperson for the emergency services in the Hamas -run enclave, said the 22-year-old was hit by a bullet and moderately wounded.
Palestinian witnesses said the shooting happened when several young Palestinians who were hunting birds approached the security fence separating the territory from Israel and came under fire. An Israeli military spokesperson confirmed there had been a shooting but claimed the wounded youth was involved in terror related activities.
"This morning terrorists attempted to conceal an explosive device in order to attack IDF soldiers who operate in the proximity of the security fence in the southern Gaza Strip," the IDF said in a statement.
After calling on them to stop and firing warning shots, the soldiers opened fire "towards the lower extremities of one of the suspects, identifying a hit."
A Palestinian was killed on Friday by Israeli gunfire in northern Gaza near the border with the Jewish state, emergency services and the news agency of the Hamas government said.
In addition, Palestinians reported that three people were injured from IDF fire after also approaching the border, near the Jabaliya refugee camp, in the southern tip of the Gaza Strip.
The IDF claim the group approached the border and were attempting to damage it. The IDF reportedly attempted to repel the group from the area, but to no avail, and the three were eventually wounded from IDF fire.
The IDF further said that in an additional border incident, forces fired on a Palestinian who approached the border fence.
Friday's causality was the third Palestinian who was killed by IDF fire in the last week.
On Wednesday, Nafa Jamil Saadi, a 22-year-old Hamas activist, was killed after Israeli security force, with the Border Guard's counter-terrorism unit, entered the Jenin refugee camp dressed as technicians to arrest an Islamic Jihad operative.
The incident ended in clashes between the two sides, and Palestinians claim that some seven additional Palestinians were wounded in Jenin.
Before hand, according to the Palestinians, Majd Lahlouh was killed after he was shot in the chest during clashes with Israeli soldiers. They said two other residents were injured.
Yoav Zitun and AFP contributed to this report