Karim Khan -- who's heading up this effort -- broke the news Monday ... saying his office is now applying for arrest warrants for each side of the conflict -- a couple for Israeli's Prime Minister including its Defense Minister, Yoav Gallant, and three on the Hamas side too.

For Hamas ... the ICC wants to arrest and charge leader Yahya Sinwar and two other high-ranking officials -- Al-Qassam Brigades and Ismail Haniyeh. All are accused of war crimes.

For the two Israeli honchos ... the ICC is alleging use of starvation as a method of warfare, plus "malnutrition, dehydration, profound suffering and an increasing number of deaths among the Palestinian population, including babies, other children, and women."

As it pertains to Hamas ... they're being accused of murder, taking of hostages, rape and sexual assault in detention -- all pertaining to the attack on Oct. 7 that kicked this all off.

Both the Hamas officials and Israeli officials are also being accused of "extermination."

Now that the top prosecutor has filed for arrest warrants -- a panel of three judges needs to weigh in ... which could take as long as two months for a decision to be handed down.

As you know ... the war has caused a massive divide across the world, including here in the U.S. -- where many young people, including college students, have protested en masse for months ... with some of the demonstrations even getting violent as they clash with cops.