No injuries to Israeli army troops were reported, the Israeli statement said.
The deaths of two of its fighters could trigger an escalation between Hamas and Israel. One Israeli soldier was killed by a Gaza sniper during this period.
The incident took place as Egypt was working to broker a cease-fire deal between Hamas and Israel. It released a video appearing to show militants shooting from a watchtower, then a tank shell hitting the position.
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According to Israel's Channel Two, following the incident, Hamas issued a statement saying, "There will be dire consequences, the occupation should not sleep quietly - the resistance can not allow the occupation to attack our positions without paying a price".
Israel says Hamas, which rules Gaza, is using the protests as cover to carry out cross-border attacks.
Israel's security cabinet discussed the proposal on Sunday, but afterwards ministers said only that the Israeli military was "prepared for any scenario".
Al-Aydi was one of four minors who died of gunshot wounds between July 27 and August 5 after Israeli forces shot them during protests on the the Gaza border. Violence between the Palestinians and Israel has gained momentum late March, when Gazans started marching towards the fenced border with Israel in a series of protests calling for the right of Palestinian refugees to return to their lands in Israel.