It was a rare instance of violence along the normally quiet border. The Egyptian side has been plagued by both criminal trafficking rings and Islamic militant groups which have affected both Israel and Egypt.
Israeli officials did not confirm the Egyptian official's account of the shooting, saying the incident was under review. The Israeli military said the Israeli was "shot and fatally wounded" by gunfire emanating from Egypt and said he died as he was being rushed to a hospital.
Israeli media reported that Abu Amar was 15 years old, an assertion the Defense Ministry did not confirm but said it was looking into.
The military said that the shooting did not appear to be related to militant activity.
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The senior Egyptian security official said the soldier mistook the Israeli for a migrant attempting to cross the border and opened fire. He said Egypt had notified Israel that the shooting was a mistake.
The official said the traffickers shot at the workers in an attempt to disrupt work on the fence. He said the shooting took place in al-Kontala, a district in Egypt known as a hub of human and drug trafficking.
The official spoke on condition of anonymity because he was not authorized to discuss the incident with the media. Israel erected the border fence in a bid to stamp out a flow of African migrants, most from Eritrea and Sudan, who pay human traffickers hefty sums to get them through Egypt's lawless Sinai Peninsula to reach Israel, often traveling under precarious conditions.
Many migrants say they are fleeing conflict and persecution and are seeking refugee status. Israel says they are economic migrants whose growing numbers threaten the country's Jewish character.