Sinn Féin has said there is no logical reason why the Government is not joining South Africa's case against Israel at the International Court of Justice.
Spokesperson on Foreign Affairs Matt Carthy said the Government previously joined proceedings at the ICJ against Russia over of its actions in Ukraine and it must do likewise now.
"What the Palestinian people require, what international law requires and what humanity requires is meaningful action," he said.
"The South African government have taken a meaningful action by bringing this case to the Hague this morning. And it is imperative in our view that the Irish Government join them in that endeavour."
Mr Carthy said that Israel continues to ignore international calls for a ceasefire in Gaza and therefore there is a need for substantive actions which Ireland should support.
"The arguments for not doing something are very crass and don't stand up to scrutiny," he said.
Ireland 'deeply concerned' Israel may have committed war crimes - Taoiseach
Taoiseach Leo Varadkar said the Government has made it "very clear in many international forums" that it is "deeply concerned" that Israel may have committed war crimes in its actions in Gaza.
However, he said that when it comes to the issue of genocide "that's a very particular matter and the International Court of Justice (ICJ) will now have to rule on that, and it may take many years before they rule on that".
Mr Varadkar added that the South African case might allow the ICJ to make an order calling for the fighting to stop while the case is considered over the next number of years.
"That's where Ireland could play a role if the ICJ issued such an order," he said.
"But also bear in mind, they have issued such an order in relation to Russia's actions in Ukraine and Russia took the decision to ignore it, and I'd be afraid that Israel would do the same."
The Taoiseach repeated the Government's call for a ceasefire in Gaza.
"That's the most important thing, that the violence should stop and that we can move towards a political solution," he said.
"And that would be a two-state solution, with the Palestinian state being established."
Tánaiste denies Govt out of step with public opinion
Meanwhile, Tánaiste Micheál Martin has defended the government's position.
Speaking in Colombia, Mr Martin denied that the Government was out of step with public opinion.
He said he was "taken aback" by some of the commentary of some in opposition this week in relation to the genocide issue.
"I don't think it's good enough frankly and we can agree to disagree with the opposition's position on this, but this kind of approach of trying to create division within Ireland is one which I don't think is the correct approach or is fair in terms of the assessment of Ireland's positions on the Middle Eastern issue and the Israel/Palestine conflict," he said.
Mr Martin said it was important for Israel to be held accountable for its actions in Gaza but equally that it was important to hold Hamas to account for some of the "horrific violations that they have engaged in".
"Right now obviously it's a preliminary hearing and the court will make a provisional recommendation," Mr Martin said.
"We will monitor that. Our focus right now is on a humanitarian ceasefire and trying to get that.
"Most main actors in the region are focusing on the absolute necessity of a human ceasefire and secondly the avoidance of a regional escalation.
"That's our focus right now and we will continue to monitor what's happened at the ICJ in terms of the genocide convention."
Difficult for the court to ignore the evidence
Professor Ray Murphy from the Irish Centre for Human Rights, University of Galway said this was a very significant case and that genocide was a sensitive subject in Israel.
"It'll take some years for the court to actually deliver its decision," he said.
Speaking to RTÉ's News at One, Prof Murphy said the court could agree provisional measures to order Israel to do certain things to prevent genocide taking place.
He said he expects there will be provisional measures if there is a finding, but he does not expect Israel to pay much heed to them.
Prof Murphy said it would be difficult for the court to ignore the evidence and not to make appropriate orders of provisional measures against Israel.
He said that they must find whether there is a real risk or evidence of genocide taking place.
"Enforcement remains a major weakness in the legal framework governing all international crimes," he added.
Despite this, he said it would be extremely embarrassing for provisional measures to be ordered against Israel, and also embarrassing for the US.
The court has to prove an intent by Israel to destroy the Palestinian population, but he said that this has been seen in public statements made by politicians, military officers and other public figures in Israel.
He said that people there had been warned to stop making such statements, as it is an international crime to incite anyone to commit genocide.
