On Friday, Palestinian journalist Yasser Murtaja was fatally shot in Gaza where he was covering the confrontation between Palestinian protesters and the Israeli Defense Force (IDF).
"Son of a bitch!" one soldier said in celebration.
ICC prosecutor Fatou Bensouda noted that 27 Palestinians have reportedly been killed by the IDF in the last fortnight and more than 1,000 have been injured - "many, as a result of shootings using live ammunition and rubber bullets".
He was carrying a video camera and wearing a flak jacket marked with the word "press" when he was shot.
Murtaja was about 300 yards away from the Israeli border fence filming Palestinians burning tires when Israeli soldiers shot him, said Palestinian photographer Rushdi Serraj, who worked with Murtaja and was with him when he was shot.
Yousef Munayyer, who directs the U.S. Campaign for Palestinian Rights, pointed out how extreme Israel's rules of engagement now are, in permitting lethal fire to be used against protesters who even approach its perimeter fence around Gaza.
Yohanan Plesner, head of the nonpartisan think tank the Israel Democracy Institute and a captain in reserves for an Israeli special forces unit, said he believed Lieberman's claim of Murtaja's Hamas affiliation.
The shooting appears to take place along the Gaza Strip border with Israel, with one of the voices in the video declaring in Hebrew: "Wow".
The Palestinian seems to be near the fence dividing the Gaza Strip from Israel, but does not appear to pose an immediate threat.
It said Tuesday an initial probe shows the video was taken in December during "violent riots".
"I can't fire because of the barbed wire", the sniper replied.
Israel confirmed the strikes, saying they were retaliation for gun fire.
It said a single bullet was sacked toward the Palestinian "suspected of organising and leading this incident while he was a few metres from the fence", wounding him in the leg.
His statement comes after fresh violence on Friday when nine Palestinians were killed by Israeli occupation forces during border protests. There have been no Israeli casualties.
Palestinian health authorities say nearly 1,300 folks are taken and wounded by Israeli soldiers during the mass boundary protests, known due to the land Hamas rulers.
The International Criminal Court's prosecutor, Fatou Bensouda, warned both Israel and Hamas that each could be committing crimes - as if a terror group using violence to breach a border and a nation defending itself are equivalent.
The video was met with outrage internationally and from Palestinians and Israelis.