It said Ahmad Morjan and Abed el-Hafeth el-Sillawi, both aged 23, were killed in the shelling, adding that no injuries were brought to hospital.
Israel says Hamas, which rules Gaza, is using the protests as cover to carry out cross-border attacks.
The Palestinian news agency Wafa reported that the incident was "expected to destroy Egypt and the UN's efforts to achieve a long-term ceasefire" between Israel and Hamas. The video then cuts to separate footage of a shell hitting the post and an explosion.
"The resistance can not allow the occupation to impose a policy of bombing sites and targeting fighters without paying the price", it said in a statement.
Perseid meteor shower to take place this weekend
As many as 100 meteors, or shooting stars, can be seen per hour during the shower's peak between Saturday and Monday. Every year, as Earth passes through the Swift-Tuttle's tail of debris, the Perseid meteor shower occurs.
Israel's security cabinet discussed the proposal on Sunday, but afterwards ministers said only that the Israeli military was "prepared for any scenario".
About 158 Palestinians have been killed and more than 17,000 others injured by Israeli gunfire during the rallies, which take place every Friday.
In the past four months, there has been an upsurge in violence along the Gaza-Israel border.
Israel has lost tracts of farmland and forest to fires started by kites and helium balloons laden with incendiary material which have caused fires in Israeli forests and farmlands and flown over the border by Palestinians in Gaza. Israel has said they only opened fire in self-defence or on people trying to infiltrate its territory.
The report noted that the Israeli violations against Palestinian information freedoms increased sharply compared to the same period past year which witnessed 127 violations.