The court has been asked by the UN General Assembly to give a so-called advisory opinion on the legal consequences of what Israel calls an "anti-terrorist fence".
Israel has consistently rejected the ICJ's competence in the matter, arguing the court should not rule on what it regards as a purely political issue and asserting their fundamental right to self-defence.
But international law expert Olivier Ribbelink, of the TMC Asser Institute for legal studies in The Hague, dismissed Israel's arguments.
"In my mind there is no doubt that this is a legal question," he said.
"It relates to very specific issues in international law - the extent of self-defence, the obligation of an occupying power towards the civilian population and the significance of decisions by the UN Security Council and the General Assembly."
And Heikelina Verrijn Stuart, a Dutch lawyer, said it is highly unlikely the court will follow arguments that it is inappropriate to rule on the issue because it is a political question that should be dealt with in the UN.
"I think that after so many years of resolutions from both the General Assembly and the Security Council against Israel it is a little weak for the court to say that the case should be left to the UN," she said.
"No one would blame (the Israelis) for building a wall along the borders of their sovereign state. I do not see how the building of a wall on Palestine territory could be justified as a security measure"
However, Israel is not only fighting the competence of the court but also focusing on its right to self-defence.
Tel Aviv says the wall, which mostly consists of wire fencing but in some places also of 8 metre-high cement slabs, is necessary to prevent "suicide" attacks from the Palestinian territories.
But experts say the controversial path of the barrier - which at points juts deep into the West Bank and does not follow the Green Line (the 1949 armistice line between Israel and the Palestinian territories) will be central in the case if the court rules it is competent.
"No one would blame (the Israelis) for building a wall along the borders of their sovereign state. I do not see how the building of a wall on Palestine territory could be justified as a security measure," John Dugard, the special rapporteur of the United Nation's commission on human rights in the occupied Palestinian territories, said.
Experts believe the Fourth Geneva Convention, which states what you can do on occupied territory and the responsibilities of an occupying power towards the civilian population, will be at the core of the case before the ICJ.
Israel argues the Geneva convention does not apply to the West Bank because Israel is not an occupying power as it is the only state to claim sovereignty over the territory.
Despite advancing many legal arguments to support its case, Israel appears resigned to the fact that it will lose before the ICJ.
Last week Israeli Justice Minister Yossef Lapid said he expected a "negative ruling for Israel".
Meanwhile, human rights group Amnesty International has added its voice to the growing number of organisations opposing the wall on the eve of the hearings.
Amnesty called on the Israeli authorities to immediately dismantle the sections of the wall already built inside the West Bank and halt construction inside the occupied territories.
It said most of the wall is not being built on the Green Line between Israel and the West Bank.
"Close to 90% of it is on Palestinian land inside the West Bank, encircling Palestinian towns and villages and cutting off communities and families from each other," Amnesty said.
"It separates farmers from their land and cuts off Palestinians from their places of work, schools, health care facilities and other essential services...
"Close to 90% of it (the wall) is on Palestinian land inside the West Bank, encircling Palestinian towns and villages and cutting off communities and families from each other. It separates farmers from their land and cuts off Palestinians from their places of work, schools, health care facilities and other essential services"
"Israel's legitimate needs to secure its borders and prevent access to people who may constitute a threat to its security do not justify the building of such a fence/wall inside the occupied territories."
The rights group said the building of the wall inside the occupied territories has severe negative consequences for hundreds of thousands of Palestinians.
It imposes unprecedented disproportionate and discriminatory restrictions on their movements within the occupied territories and causes other violations of their fundamental rights, including the right to work, to food, to medical care, to education and to an adequate standard of living.
The route of the wall has been designed to encompass more than 50 Israeli settlements in the occupied territories, in which the majority of Israeli settlers live and which are illegal under international law.
Amnesty said: "International human rights and humanitarian law requires Israel, as the occupying power, to protect and ensure the rights of the Palestinian population in the occupied territories."