Prime Minister Benjamin Netanyahu said the decision made the Hague-based court, which Israel has refused to sign up to since its creation in 2002, a "political tool" against the Jewish state.
The Palestinians welcomed the move by the ICC as a "long overdue step" following a nearly five-year preliminary probe by the prosecutor into the situation since the 2014 war in Gaza.
"I am satisfied that there is a reasonable basis to proceed with an investigation into the situation in Palestine," ICC prosecutor Fatou Bensouda said in a statement.
"In brief, I am satisfied that war crimes have been or are being committed in the West Bank, including East Jerusalem, and the Gaza Strip," she added, without specifying the perpetrators of the alleged crimes.
She said that before opening a full probe, she would ask the ICC to rule on the territory over which it has jurisdiction because of the "unique and highly contested legal and factual issues attaching to this situation."
"Specifically, I have sought confirmation that the 'territory' over which the Court may exercise its jurisdiction, and which I may subject to investigation, comprises the West Bank, including East Jerusalem, and Gaza."
She urged judges to rule on the court's jurisdiction "without undue delay".
The prosecutor added however that she did not require any authorisation from judges to open a probe as there had been a referral from the Palestinians, who joined the court in 2015.
'Long overdue'
The issue is highly sensitive, with then White House national security adviser John Bolton threatening last year to arrest ICC judges if they moved against Israel or the United States.
Israel and the United States have both refused to sign up to the court, which was set up in 2002 to be the only global tribunal trying the world's worst crimes, war crimes and crimes against humanity.
Bensouda launched a preliminary probe in January 2015 into allegations of war crimes and crimes against humanity in Israel and the Palestinian territories, in the wake of the 2014 Gaza war.
A full ICC investigation could possibly lead to charges against individuals being brought. States cannot be charged by the ICC.
"Palestine welcomes this step as a long overdue step to move the process forward towards an investigation, after nearly five long and difficult years of preliminary examination," the Palestinian statement said.
Netanyahu however lashed out at what he called a "dark day for truth and justice".
"The ICC prosecutor's decision has turned the International Criminal Court into a political tool to delegitimise the State of Israel," he said.
The ICC's preliminary investigation has looked at the 2014 war which left 2,251 dead on the Palestinian side, the majority civilians, and 74 on the Israeli side, most of them soldiers.
It has also looked at violence near the Israel-Gaza border in 2018.
Earlier this month, the ICC prosecutor refused to press charges over a deadly 2010 Israeli raid on a flotilla bringing aid to Gaza, and urged that probe to be shut.
Nine Turkish citizens died in May 2010 when Israeli marines stormed the Mavi Marmara, among eight ships trying to break a naval blockade of the Gaza Strip. One more died in hospital in 2014.
Agencies contributed to this report.
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