Ireland and Jordan were among 49 countries and three organizations that are addressing the court during the six-day process that began February 19 and is expected to end this coming Monday.
Israel, which is not taking part, said in written comments that the court's involvement could be harmful to achieving a negotiated settlement.
Time and time again, international bodies have attempted to investigate and hold Israel accountable for alleged war crimes.
This is the second day of a six-day hearing on the dispute between Israel and Palestinians.
85 voted in favor, five less than the required amount.
The ICJ is expected to hear half-hour statements from 49 countries and three international organizations, in addition to the PA’s three-hour legal argument presented Monday.
"Many of the Christian community are deeply unhappy about the allegations being leveled by our government on Israel," explained Philip Rosenthal, director of ChristianView Network.
A weekly selection of opinions and analyses from the Arab media around the world.
The decision comes after South Africa asked the World Court to consider whether Israel's plan to extend its offensive in Gaza into the city of Rafah requires additional emergency measures.
"We are gravely concerned by indications that Israel is planning a ground offensive into Rafah. A military operation into Rafah would be catastrophic," the statement said.