Taoiseach Leo Varadkar and Spanish Prime Minister Pedro Sanchez have written to President of the European Commission Ursula von der Leyen, expressing deep concern at the deteriorating situation in Gaza.
The pair have also called for an urgent review of whether Israel is complying with its human rights obligations under the EU/Israel Association Agreement.
They asked the commission to propose appropriate measures to be taken by the European Union if it considers that Israel is in breach of the agreement.
The expanded Israeli military operation in the Rafah area poses a grave and imminent threat that the international community must urgently confront, the letter says.
But the Taoiseach told the Dáil that any suspension of the agreement "may well require unanimity" of EU member states.
He rejected a claim by Independent TD Catherine Connolly that Israel's actions were being done in Ireland's name.
"I don't accept we are standing idly by," he said.
"When I meet representatives of the Palestinian Authority, when I meet leaders of other Arab countries they thank us for the stance we are taking.
"We have to make sure we bring people with us, not people who already agree with us."
Ms Connolly said that in the last four months "we stood idly by while genocide was perpetrated in our name."
The leaders reiterated their total condemnation of Hamas's terrorist attacks of 7 October and Israel's right to defend itself, but insist that this must be in line with international law and international humanitarian law, including in the obligation to protect civilians.
An immediate humanitarian ceasefire is urgently needed to prevent irreversible harm to the people in Gaza, Mr Varadkar and Mr Sanchez said.
They also recalled the provisional measures adopted by the ICJ, which require Israel to take immediate and effective measures to enable the provision of urgently needed basic services and humanitarian assistance in Gaza.
UNWRA, the embattled United Nations agency tasked with helping Palestinian refugees, must be allowed to continue its vital work saving lives and addressing the catastrophic humanitarian situation in Gaza, they said.
The letter added that EU support to UNWRA must be maintained, saying there is no pathway to achieving the urgent massive and sustained scale-up in humanitarian assistance without UNWRA playing a central role.
The European Commission confirmed that it has received the letter and said it would study it before commenting in detail.
Commission spokesperson Nabila Massrali said: "We do urge all sides when it comes to Israel to respect international law and we note that there must be respect, that there must be accountability for violations of international law, that the EU consistently underlines the importance of ensuring the protection of all civilians at all times in line with international humanitarian law and it deplores all loss of civilian lives.
"The EU continues to pass these messages in all its statements as well, bilaterally in its contacts with the Israeli authorities."
The Taoiseach told the Dáil that he hopes a ceasefire will be in pace in Gaza by St Patrick's Day.
Mr Varadkar said that he will use his visit to Washington DC to tell Joe Biden of his and the Irish peoples' concerns, both in public and private meetings with the US President.
Speaking on RTÉ's News at One, Green MEP Grace O'Sullivan said the EU/Israel Association Agreement was very important to Israel and that the Green group have been calling for it to be suspended for a number of years because of the situation in Palestine.
She said that Article 2 of the agreement stipulates that the relationship between the EU and Israel must be based on human rights and she welcomed the initiative being taken by Mr Varadkar and Mr Sanchez.
"Israel has shown complete disregard for human rights in Gaza," Ms O'Sullivan said.
"We need Israel to realise that the international community says what is happening is not to be tolerated, enough is enough."
She said that if the agreement is stopped there would be enormous economic pressure on Israel.
"It would be a huge step for the EU to unite around this association agreement and stopping it," Ms O'Sullivan said.
"We have been calling for a ceasefire, a humanitarian ceasefire and now we are calling for an EU arms embargo. The impact on Israel would be enormous and that might be just what we need to stop the atrocity that is happening at the moment.
"It will put a spotlight on Ursula von der Leyen to take action."
Additional reporting Tony Connelly and David Murphy
