The ICC's chief prosecutor announced on 3 March that she had opened a full investigation into the situation in the Israeli-occupied territories, infuriating Israel, which is not a member of The Hague-based court.
Read more: Israel threatens sanctions on Palestinians over ICC probe: reports
The ICC sent a deferral notice on 9 March, which gave Israel and the Palestinian Authority a month to tell judges whether they are investigating crimes similar to those being probed by the ICC.
Had Israel informed the court that it was in fact carrying out its own probe into alleged war crimes perpetrators, it could have asked for a deferral.
A day before the deadline, Israeli Prime Minister Benjamin Netanyahu's office issued a statement saying the government had agreed "to not cooperate with the (ICC)."
The statement said Israel would send a letter to the court "completely rejecting the claim that Israel commits war crimes."
The letter will also "reiterate Israel's unequivocal position that The Hague tribunal has no authority to open an investigation against it."
Read more: Is the ICC the new frontier of Israeli exceptionalism?
The Palestinians, who have been a state party to the ICC since 2015, have welcomed the investigation and said they will not seek any deferral.
The world's only permanent war crimes tribunal, the ICC was set up in 2002 to try the humanity's worst crimes where local courts are unwilling or unable to step in.
ICC prosecutor Fatou Bensouda has said her investigation will cover the situation in the blockaded Gaza Strip along with the Israeli-occupied West Bank and east Jerusalem since 2014.
It will mainly focus on the 2014 Gaza War but also look at the deaths of Palestinian demonstrators from 2018 onwards.
Netanyahu, a vocal critic of the ICC, has said the decision to open the probe was the "essence of anti-Semitism" and declared Israel was "under attack".
However, Thursday's statement marked the first time Netanyahu had made it clear Israel would not directly engage with the ICC.
The United States has also criticised the ICC investigation and voiced support for its ally Israel.
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