Whatever the decision of the ICJ, the judgement in the court of world opinion remains at least as important, with both sides battling hard on the propaganda front.
Pro-Palestinian activists on Monday are holding protests at The Hague in the Netherlands, site of the court proceedings, and in the occupied territories. These follow several days of demonstrations by anti-wall campaigners and counter protests in Israel and elsewhere.
"It's like a media battle," says Amira Silmi of the grassroots Palestinian group Stop the Wall. Silmi tells Aljazeera.net the global attention that the court proceedings will attract gives her colleagues an important opportunity to "raise the Palestinian voice".
For their part, the Israelis have rejected the court's jurisdiction, but not the publicity its deliberations will generate – it has shipped over the wreckage of a bus destroyed by a Palestinian bomber to The Hague to publicise their concerns.
That Israeli exhibition was given added poignancy when a blast on a packed west Jerusalem bus during Sunday morning's rush hour killed the bomber and seven passengers, and wounded more than 60.
Seven Israelis were killed and 60
wounded in west Jerusalem
Israel's Foreign Minister Silvan Shalom said the attack justified the construction of the barrier. "That is why we will go on building this fence because it saves lives," he said.
But Palestinians have argued that the construction of the much criticised "apartheid wall" on their occupied land generates so much anger that it makes such attacks more likely.
Nonetheless, for many obversers, including supporters of the Palestinians, the bombing a day before the ICJ began its hearing on the wall was poorly timed.
Vying for sympathy
Sunday's attack was claimed by al-Aqsa Martyrs Brigades, an offshoot of Palestinian President Yasir Arafat's Fatah faction. It had been promising to retaliate after an Israeli raid in the Gaza Strip two weeks ago left 15 Palestinians dead.
But Palestinian Prime Minister Ahmad Quraya condemned the bombing, and acknowledged that such incidents weakened international sympathy for his people.
ID checks in Abu Dis - a town cut
in two by the separation barrier
The Palestinian leadership also alleged the bombing was carried out to damage its case at the world court deliberately.
Israel, backed by the United States and the European Union, has refused to recognise the court's jurisdiction - a defiant stance that has riled many critics.
But it recognises the public relations contest under way. A request to display pictures of hundreds of Israeli bomb victims in The Hague was turned down. But Dutch authorities have allowed the wreckage of bus number 19 blown up by a Palestinian bomber in Jerusalem last month to be exhibited.
Meanwhile, anti-wall campaigners have organised a photograph exhibition at The Hague to highlight "the impact of the wall on Palestinian lives", says Silmi.
It shows children trying to pass through the wall to reach their schools, farmland cleared to make way for the barrier, closed gates and so on.
Israel says it needs to build what it describes as a "security fence" to stop human bombers crossing its internationally recognised border. Israelis quickly seized on the fact that the wall near Jerusalem is not yet complete.
"There is absolutely no doubt that the establishment of the
barrier will really help us here in Jerusalem and elsewhere," the city's police chief Micky Levy said.
But Palestinians and their supporters say the wall is part of the problem, not the solution. They point out the wall cuts through occupied Arab lands and villages, separating farmers from their crops, businesses from markets and so on.
Moreover, the wall's route has caused widespread alarm and scepticism about Israel's claims about enhancing security.
The barrier snakes through occupied Palestinian territory rather than along Israel's recognised border – a thinly disguised attempt to encompass illegal Jewish settlements and annex more Palestinian land, say critics.
As a result, the wall has stoked anger and resentment, they say, with the violent results seen on Sunday.
But although such bombings deal the Israelis a physical blow, the Palestinian leadership is left counting the cost in public relations terms.