Around 35-40 Irish passport holders remained in the territory on Sunday and none had been included on the lists of international citizens able to leave through the Rafah crossing to Egypt.
Tanaiste Micheal Martin insisted Israeli authorities and officials in Egypt were helping Irish diplomats in their efforts to get the citizens out.
Ireland has been critical of the Israeli bombardment of the Gaza Strip.
Last week, premier Leo Varadkar said some of Israel’s actions in Gaza were not just self-defence and resembled “something more approaching revenge”.
The Taoiseach conceded that Israel would not consider Ireland a close friend or ally, as it has a different stance on Palestine than most western countries.
A far-right member of Israel’s cabinet was quoted at the weekend as saying Palestinians in the Gaza Strip could “go to Ireland or the desert”.
Mr Martin was asked on Sunday whether Ireland’s political stance was a factor in the difficulties it was encountering getting its citizens out of the territory, with Israel potentially seeking to punish the Irish Government.
“We’ve no evidence for that at all,” he told RTE.
“But we’ve been working with Israeli authorities. We’re not on the list (of people leaving via the Rafah crossing). We weren’t on the list in the last number of days. That’s just a fact.
“But we will work on a continuing basis to get our citizens out.”
Mr Martin stopped short of repeating Mr Varadkar’s reference to “revenge”, but he described the situation in Gaza as “appalling” and said war crimes could have been committed.
“This war is bringing nothing but death and misery and it has to stop, and it should stop,” he said.
“We certainly could be watching war crimes unfolding. The International Criminal Court has jurisdiction, its prosecutors made that clear, in the Middle East. And I believe there should be full accountability for what is happening here.
“I’ve always been of the view that the bombing of dense urban areas, inevitably, there’s no question, you cannot do it without killing civilians and killing children. And I don’t believe there has been any proportionality attached to this, it’s disproportionate by any measure, and it’s not necessary.”
Mr Martin also reiterated his condemnation of the Hamas attacks on Israeli citizens on October 7, describing them as “savage, brutal and barbaric”.
“The anger and the right of Israel to take on Hamas and to address the Hamas challenge, yes, they have that right,” he said.
“But it’s the pursuit and the manner and the methodology I think people are questioning. You cannot take all the civilian population along with that. You can’t make calculations that ‘if I get one Hamas commander, it’s OK to take out 100 civilians’.”
Mr Martin again declined to comment on reports from the Middle East that one of the hostages being held by Hamas could be an Irish citizen.
Ireland’s main opposition party, Sinn Fein, has called on the Government to revoke the credentials of Israel’s ambassador in Dublin, Dana Erlich, amid the bombardment.
Mr Martin criticised that demand as “populist” and “knee jerk”, insisting it would harm efforts to get Irish citizens out of the Gaza Strip.
On Sunday, Sinn Fein TD Eoin O Broin defended his party’s stance.
“At a certain point in time, given the fact that we now have 10,000 people dead, 2,000 people unaccounted for, you have to start using every single means available to you to put pressure, and so far, despite the fact that rightly the Irish Government and the majority of us in opposition have called for a ceasefire, the government in Israel is simply not listening and, therefore, the Israeli ambassador’s position is simply no longer tenable while this onslaught continues,” he told RTE.
More pro-Palestinian demonstrations took place on the island of Ireland over the weekend.
In Dublin on Sunday, a horse-drawn hearse carrying a coffin filled with children’s shoes led a protest procession that passed the US and UK embassies and the European Commission offices.
The stunt was organised to highlight the children who have died in the violence, with participants accusing the US, the UK and the EU of supporting Israel’s military action.
In Belfast on Saturday, thousands of pro-Palestinian activists marched from Queen’s University to the US consulate in the south of the city.
A rally was held at a barrier on the road leading to the consulate, while five organisers were permitted to walk to the gates of the building to hand a letter of protest to a police officer, who took it inside.
The rally heard speeches and chants condemning Israel’s actions in the Gaza Strip and US support for the Israeli stance.
At the close of the event, several children left teddy bears close to the barrier to signify the young lives lost in the conflict.
Belfast and Dublin have also witnessed pro-Israeli demonstrations in recent weeks.