The application goes further than a 2015 request for prosecutors to examine alleged crimes in the region and could fast-track the process to a full investigation.
About 600,000 Israelis live in over 230 illegal settlements built since the 1967 Israeli occupation of the Palestinian territories of the West Bank and East Jerusalem (al-Quds).
Last Monday, tens of thousands of Palestinians rallied near Israel's border fence to protest a blockade of their territory and the move of the US embassy from Tel Aviv to al-Quds that day.
The Gaza Health Ministry said over 60 Palestinians were killed and more than 2,700 others injured, including 1,360 by live fire.
It was the deadliest day in Gaza since a 2014 cross-border war.
On Saturday, two Palestinians who had been injured in the demonstrations died of their wounds, according to the ministry, bringing the death toll of the protests against the US embassy move to al-Quds (Jerusalem) and marking Nakba Day to 64.
US President Donald Trump announced on December 6 that his administration would begin the process of moving the American embassy in Tel Aviv to Quds.
After months of global outcry, the US opened its embassy in Quds in a ceremony attended by a White House delegation and Israeli regime officials on May 14.