Israeli prime minister Benjamin Netanyahu, accusing the court of anti-Semitism, described its decision to launch an investigation as "outrageous," telling Fox News, "I am going to fight this in every place."
The court's outgoing prosecutor, Fatou Bensouda, said on Wednesday her office will formally investigate war crimes in the Israeli-occupied West Bank, Gaza and East Jerusalem al-Quds after the court accepted jurisdiction last month.
Bensouda has identified the Israeli military's use of lethal and non-lethal force against Palestinians demonstrating near the fence separating the Gaza Strip from the occupied territories after 2018 as one possible focus of the investigation.
One of those killed in the protests was Raza al-Najar, a 21-year-old volunteer medic shot by Israeli troops in June 2018 at a protest near Khan Younis in southern Gaza.
Her mother welcomed the decision, calling it "a victory for (all) Palestinians."
"I hope the ICC achieves justice for my daughter, Raza, and for all other martyrs Israel has killed," Sabreen Al-Najar, 47, told Reuters. "I hope the court takes it seriously, and that it reveals the truth behind the Israeli occupation."
The Israeli military claims Najar was killed inadvertently by Israeli troops after being struck by a bullet that ricocheted.
Rejecting the court's jurisdiction, Israel's UN ambassador said Israeli leaders might try to persuade the tribunal's newly-elected prosecutor, Karim Khan of Britain, who takes office on June 15, to shift the ICC's focus.
The ICC investigation is "not logical or moral," Gilad Erdan told Israel's Army Radio.
Erdan said the inquiry could put senior Israeli military officers, commanders and politicians under threat of arrest if they traveled abroad.
Palestinian President Mahmoud Abbas issued a statement on Thursday, calling the investigation a defense of "rights and freedoms" and saying it also covered Israel's 2014 war and Israeli settlement building in the occupied West Bank.