Since the protests began, Israeli forces have killed more than 140 Palestinians in the besieged coastal enclave and wounded more than 16,000 people, according to health officials in Gaza.
Yousef Munayyer, executive director of the U.S. Campaign for Palestinian Rights, added: "Israeli snipers shoot and kill scores of unarmed Palestinian protesters in Gaza, including kids, then calls it self-defense".
A senior Hamas official, speaking on condition of anonymity, told AFP the deal involved "the cessation of all forms of military escalation" including Israeli air strikes and Hamas mortars and rockets.
"There has been no calm in Gaza for many, many decades", she said.
Hamas rulers said Saturday they had accepted a cease-fire ending a massive Israeli onslaught on militant positions after a soldier was shot dead, once again pulling the sides back from the brink of a full-fledged war.
On Friday an Israeli soldier was shot dead by Palestinian fire along the border, the first killing of a soldier in and around Gaza since a 2014 war between Hamas and the Jewish state.
"The event that happened today is something that we can not tolerate and can not allow to become a routine norm, that's why we retaliated and that's why we continue to target military targets belonging to Hamas", said Lieutenant-Colonel Jonathan Conricus, an Israeli military spokesman.
"With Egyptian and United Nations efforts it has been agreed to return to the era of calm between (Israel) and Palestinian factions", said Fawzi Barhoum, spokesman for the Hamas Islamist group that controls Gaza.
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Israeli warplanes carried out several airstrikes reportedly targeting Hamas sites across different areas of the besieged Gaza Strip on Friday evening.
A ceasefire announced by Hamas largely held on Saturday after a wave of deadly air strikes across the Palestinian enclave sparked by the death of an Israeli soldier shot near the border.
Israel has said it is defending its sovereign border.
Israel's Prime Minister Benjamin Netanyahu met with Army Chief of Staff Lt. Gen Gadi Eizenkot and Mr. Lieberman at the military's headquarters in Tel Aviv to discuss the escalating tensions in Gaza.
The airstrikes came after the Israeli army declared the beginning of a widespread attack across the Gaza Strip in response to fire opened at Israeli soldiers in the eastern Gaza Strip earlier.
Israeli politicians have been calling for a fierce response to the kites and balloons, which have caused damage amounting to millions of shekels (hundreds of thousands of dollars).
Last weekend saw the most severe exchange of fire in Gaza since a 2014 war.
Lieberman has raised the threat of a large-scale operation in the Gaza Strip if Hamas does not stop the kites and balloons being launched.