President Michael D Higgins has suggested Israel and countries that supply it with weapons should be excluded from the United Nations.
He described an independent UN commission report, which concluded that Israel has committed and continues to commit genocide against Palestinians, as a "very, very important document".
Mr Higgins said: "I believe myself that the kind of actions that are necessary now are the exclusion of those who are practising genocide, and those who are supporting genocide with armaments.
"We must look at their exclusion from the United Nations itself, and we should have no hesitation any longer in relation to ending trade with people who are inflicting this at our fellow human beings."
President Higgins said some of the EU's strongest members are "deciding to stay silent in watching emaciated children in what is a human, manmade, really atrocious infliction on people" in Gaza.
He said he believes the "EU will find it extraordinarily difficult to ever be a union in any sense" when these members are staying silent.
Speaking at the National Ploughing Championships, President Higgins said: "I think it's a very, very important document, and of course the chair of that working group was the chair of the working group on Rwanda, and it explicitly states that four of the main actions as referred to in the 1948 convention on genocide, are met."
UN report a 'very important document', says President Higgins
"It goes further and suggests that the incitement to genocide has been present and it specifically mentions those in high office who use language to encourage and to incite genocide," he said.
President Higgins said half of all "the people killed yesterday and today" were women and children.
Israeli President Isaac Herzog, who was named in the report, condemned its findings, which he said misinterpreted his words.
Israel has repeatedly criticised the work of the commission, with officials labelling its reports "blood libel".
'Definitive and significant' report, says Taoiseach
Meanwhile, Taoiseach Micheál Martin described the report as "definitive and significant".
Speaking at the Fianna Fáil think-in in Douglas, Co Cork, he said it was "very clear genocide is taking place" in Gaza.
He said: "It's a very serious report, I welcome the report in terms of how comprehensive it is, how fact-based it is."
"And the head of that report was also involved in the report on the genocide in Rwanda and no one questioned their judgement on that occasion," Mr Martin added.
UN report on Gaza 'definitive and significant' - Taoiseach
"So this is a very definitive and significant report, and we await the findings of the International Court of Justice which South Africa filed, and we intervened on that case."
"That report is saying four of the five criteria have been met in respect of Israel’s behaviour in Gaza and we all are witnessing it now," said the Fianna Fáil leader.
"Every residential tower block is being destroyed.
"That report says 90% of all housing has been destroyed, education facilities have been destroyed, healthcare facilities, fertility facilities are being destroyed - in other words you’re attacking birth."
Mr Martin called for the wider world to raise the pressure on Israel to "stop this carnage" and the "slaughter of civilians".
He said: "So it’s very, very clear from that report that a genocide is taking place and Israel, and the government of Israel, will have to be held to account for what is happening."
"And the atrocity carries on - the Israel defence minister this morning declared that 'Gaza City is burning’ - what kind of mentality is informing Israeli government behaviour?
"In my view, the US, Europe and wider world have to raise the pressure to stop this carnage and the slaughter of civilians.
Read more: Israel launches huge ground assault on Gaza City
"And yes the hostage should be released without condition by Hamas, release the hostages and end this carnage."
Meanwhile, the European Union has warned that Israel's ground assault on Gaza City will add to the toll of death and destruction, and worsen an already "catastrophic" humanitarian situation in the territory.
"The EU has consistently urged Israel not to intensify its operation in Gaza City," EU spokesman Anouar El Anouni said.
"A military intervention will lead to more destruction, more death and more displacement, and we have been clear that this will also aggravate the already catastrophic humanitarian situation and also endangers the lives of hostages."
The United Nations rights chief also condemned Israel's ground assault as "totally and utterly unacceptable" and demanded an end to the "carnage".
"The whole world screams for peace. Palestinians, Israelis scream for peace. Everyone wants an end to this, and what we see is a further escalation which is totally and utterly unacceptable," Volker Turk said.
"It is absolutely clear that this carnage must stop."
'Crucial' EU goes ahead with Israel sanctions, says Harris
Tánaiste Simon Harris has said it is "absolutely crucial" that the European Union moves ahead with sanctions on Israel.
Speaking at the National Ploughing Championships, Mr Harris welcomed an independent UN commission report, which concluded that Israel has committed and continues to commit genocide against Palestinians.
"I welcome the light that the UN enquiry has shone on what is a genocide in Gaza," Mr Harris said.
He added: "We've been saying that in this country for a long time, I remember when I was Taoiseach last year, when I became the first European head of government to say that this was and is a genocide - now an inquiry has determined that as well.
"It’s shown to be true what the Irish people have known in their hearts and witnessed with their eyes on the television screens to be true.
"It’s now absolutely crucial that the European Union moves ahead with sanctions, we’ve been pushing this for a long time.
"There are things we can do at a domestic level, and we should and we will, but none of that will be in any way as impactful as the European Union together taking decisions."
Additional reporting: AFP and PA
