Prosecutor Fatou Besouda added that before doing so she would ask the Hague-based tribunal to rule on the territory over which it has jurisdiction, as Israel is not a member of the court.
"I am satisfied that there is a reasonable basis to proceed with an investigation into the situation in Palestine," 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."
The statement did not specify the perpetrators of the alleged crimes.
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.
The issue is highly sensitive, with 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.
The Palestinians, who signed up to the ICC in 2015, have already accepted the court's jurisdiction but have repeatedly urged the court to move faster.
A full ICC investigation could possibly lead to charges against individuals being brought. States cannot be charged by the ICC.
The nearly five-year 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. – Rappler.com