The meeting at the ICC comes after more than 60 Palestinians protesting the United States decision to move its embassy from Tel Aviv to the disputed city of Jerusalem were killed by Israeli fire last week.
The Palestinians returned to the ICC in the aftermath of accelerated settlement activity in which Israel advanced plans for over 10,000 new homes in 2017. The foreign minister emphasized on an investigation alleging that grave crimes are being committed by Israel against the Palestinian people.
The Al-Awda, Arabic for The Return, vessel set sail a week ago from Norway and linked up with three other boats in Copenhagen, Denmark on Sunday, before beginning a tour of European ports which will end in the Gaza Strip.
Israel, which came under intense global scrutiny over its handling of violence on the border on Monday and Tuesday, has accused Hamas of using the several weeks of mass protests as a cover for launching terror attacks against Israeli troops and civilians.
Israel called the move "cynical" and claimed the request to the ICC has no legal validity.
Israel is not a member of the ICC, but its citizens can be charged by the court if they are suspected of committing crimes against a national of a country that is a member.
Speaking at a press conference in Gaza City, Krahenbuhl described the nature of injuries sustained by Palestinian protesters as "shocking".
Bensouda vowed last week that she was watching the unrest in Gaza closely and would "take any action warranted" to prosecute crimes.
Last Friday, the UNHCR opened a probe into Israeli use of live ammunition by the Israeli occupation forces. But critics say the investigations rarely lead anywhere.
"The recent killings in Gaza only underscore the importance of the ICC prosecutor acting to address the pervasive climate of impunity in Palestine", said Richard Dicker, director of the International Justice Program at Human Rights Watch.
In 2004, the U.N.'s highest judicial organ, the International Court of Justice, ruled in an advisory opinion that the settlements breached international law.
Malki said the complaint seeks an investigation into Israeli policies in the West Bank, Gaza Strip and east Jerusalem since the state of Palestine joined the ICC in June 2014. It says east Jerusalem is an inseparable part of its capital, and considers the West Bank to be disputed territory whose fate should be decided in negotiations.
The IDF also confirmed that a mini-drone from Gaza had crossed over the border fence and fallen in Israeli territory overnight Tuesday.
The probe included crimes allegedly committed by both sides in the 2014 Gaza conflict between Israel and Hamas.
Under worldwide law it is illegal to transfer populations out of or into occupied territory.