In a statement, Mrs Clooney said there were “reasonable grounds” to believe that Mr Netanyahu and Mr Gallant “have committed war crimes and crimes against humanity including starvation as a method of warfare, murder, persecution and extermination”.
She said she hoped that “justice will prevail in a region that has already suffered too much”.
A decision on whether to issue an arrest warrant will now be taken by ICC judges. Decisions historically take some months and rarely result in an arrest.
Israel is not a member of the ICC and has called for allies to leave the court’s jurisdiction over the decision.
Bezalel Smotrich, Israel’s finance minister, described the call for arrests as a “show of hypocrisy and Jew-hatred” that recalled Nazi propaganda.
“Arrest warrants against them are arrest warrants against us all,” he said.
Benny Gantz, an Israeli war cabinet minister, said the move was a “crime of historic proportion”.
“Drawing parallels between the leaders of a democratic country determined to defend itself from despicable terror to leaders of a blood-thirsty terror organisation is a deep distortion of justice and blatant moral bankruptcy,” he said.
Sami Abu Zuhri, a senior Hamas official, said that the call for the arrest of three of the group’s leaders “equates the victim with the executioner”.
The ICC has not always issued warrants demanded by its prosecutors, or for all charges brought against suspects. Countries have sometimes refused to enforce the warrants once they are issued.
However, the Labour Party said the UK would have no choice under the Rome Statute, the international law that underpins the court, but to comply with a warrant and detain him.
David Lammy, the shadow foreign secretary, said: “Labour believes that the UK and all parties to the Rome Statute have a legal obligation to comply with orders and warrants issued by the court. Democracies who believe in the rule of law must submit themselves to it.”
Mr Netanyahu said the decision was “a distortion of reality” and accused the prosecutor of spreading a “new anti-Semitism”.
He said: “With what audacity you compare between the Hamas that murdered, burned, butchered, raped, and kidnapped our brothers and sisters, and the IDF soldiers who are fighting a just war that is unparalleled in morality that is unmatched?”
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