Tánaiste and Minister for Foreign Affairs Micheál Martin has said some 90 dependents of Irish citizens in Gaza have been evacuated to date, with around 40 remaining.
He visited a United Nations Palestinian refugee camp south of the Jordanian capital Amman as he concluded a two-day visit to the Middle East.
He said the Irish authorities depended on Israel in terms of selecting evacuees, while the Egyptian side was responsible for facilitating the logistics of exiting people from the enclave.
"From the initial evacuation we had a list, which was supplied to us, [while] others have come onto the list since then, and the majority would be dependents," Mr Martin said.
"We've been responsive to that, but we don't govern the situation within Gaza.
"So the Israeli authorities decide on who can be let out.
"We do advocate on behalf of people with the Israeli authorities, and then with Egyptian authorities in terms of facilitating their exit from Gaza."
Speaking on RTÉ's Drivetime, Mr Martin said he talked to the Egyptian foreign minister yesterday on the subject, who he said wants to be "facilitative".
Some people have managed to come out of Gaza independently, he said, and the Government has facilitated their "exit from Egypt" and their reintegration into Irish society and Ireland's ambassador in Egypt is "discussing how best we can work with our ambassador in Israel to get the remaining citizens and dependants out".
Mr Martin added that some Irish medics have gone to Gaza to help and the Government would "facilitate that ...be open to discussing with Irish medics in terms of any contribution that they could make".
The Tánaiste said he visited an UNRWA (UN Palestinian refugee agency) facility in Jordan earlier and was impressed with the much "good stuff" being done at primary care level, maternal health, and vaccinations, which is why he understands cholera has been prevented so far.
But he said there was also a warning yesterday that cholera "isn't too far away now".
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Martin pessimistic over ceasefire prospects
At the end of his two-day visit, the Tánaiste said he was pessimistic about the prospects of a ceasefire in Gaza and was worried about an Israeli assault on Rafah.
He said: "Humanitarian agencies in Rafah will not be able to sustain an invasion, and there's an urgent need for the international community to make it very, very clear to Israel that an invasion cannot be countenanced.
"What we're hearing is that Israel is contemplating an invasion, and it was clear from the interaction with humanitarian workers yesterday [at the Rafah Crossing] and from others over the last two days that that would be catastrophic."
Speaking on RTÉ's Drivetime, Mr Martin said the situation at the Rafah crossing is "dire and there is an absolute need for a surge in humanitarian aid".
He said they also "identified a very significant trauma on the people of Gaza, particularly children, and they said the psycho-social trauma and repercussions of this war will be simply enormous in the aftermath of the war."
The Tánaiste had "two messages" for Israeli Prime Minister Benjamin Netanyahu, who has promised a ground offensive on Rafah.
"Please stop the unnecessary barriers to aid getting in," he said.
"We went to a depot at Rafah where we saw rejected goods: a CT scanner, a lot of hospital equipment just simply denied by the Israeli authorities on the grounds of dual use.
"A green sleeping bag because it could be used as camouflage. A children's education pack because there's a small scissors.
"Unbelieveable given the enormity of the starvation and the hunger, and there's many more, crutches for example, all being stopped and rejected - so that's the first message."
He said the second message was that Israel's planned invasion of Rafah will be "catastrophic and for the people of Gaza it will means thousands more deaths.
"It will also mean by definition that many of the humanitarian organisations, the UN organisations who are based in Rafah, that their work will be severely restricted in the context of such an invasion, with further dire consequences for people in terms of medical attention," Mr Martin said.
The Tánaiste said Jordan was making strenuous efforts to get Israel to open up a humanitarian corridor into northern Gaza, and that progress had been made in getting more aid trucks in through the south at Rafah.
"There are two or three checks nearly for every consignment," Mr Martin said.
"It is unbelievable, the barriers that have been put up against aid going into Gaza, given the enormity of the suffering, that families that people are going through."
Read more: Orders for new evacuations as strikes in Gaza intensify
Earlier, Mr Martin was welcomed at an elementary school for girls at the Talbieh camp, home to some 10,000 Palestinians and also visited a UNRWA-run medical facility.
He arrived at the Ministry of Foreign Affairs for a meeting with the Jordanian Deputy Prime Minister and Foreign Minister Ayman Safadi.
At the school, UNRWA director for external relations in Jordan, Tamara Alrifai, told RTÉ News the provision of education for some 1,300 pupils at the school had been under significant pressure once funding was cut, on foot of Israel's allegations about UNRWA staff.
"There was a real concern of funding drying up after 18 government donors, partners of UNRWA, decided to suspend funding following allegations against 12 staff members," she said.
"We continue to be very concerned about the lack of funding for an agency that, particularly in Jordan, directly contributes to stability.
"We have enough funding to last us until the end of the month of June, which coincides with the end of the school year, but we need more financial visibility in order to be able to maintain, not just education, but also healthcare [and] social protection to Palestinian refugees in Jordan and in the region."
Ms Alrifai said UNRWA fully accepted the recommendations of the Colonna report on UNRWA published on Monday, including the concerns about agency staff maintaining neutrality on the Israel-Palestinian conflict.
"We embrace them, and we are already working on implementing them," she said.
"We took note of the concerns about UNRWA as a huge bureaucracy [with] 32,000 staff.
"It takes a lot to get everybody fully compliant with neutrality. But the report rightly confirms that UNRWA does have sturdy internal system guidelines, procedures and mechanisms to ensure that our safeguards against violations of neutrality are in place.
"It's a matter of improving and continuously improving is a commitment that we do have."
She said children at the school had been affected by the war in Gaza, in particular, because many of them have relatives in the enclave.
"The children here go through a lot of interactive, play-like sessions to help them cope with what they see on TV, but what their families also tell them," Ms Alrifai said.
"Many of the children in our schools have relatives in Gaza because this is where they're originally from. Teachers are very well equipped to deal with the psychological impact and to help children overcome them.
"But that is also a reason why funding to run must continue. So that psychosocial support doesn't become a luxury but continues being part and parcel of our education."
Tánaiste welcome's Germany decision to resume UNRWA funding
The German government has announced it plans to resume cooperation with UNRWA in Gaza following the Colonna report, according to the foreign and development ministries.
The Colonna review of the agency's neutrality on Monday concluded Israel had yet to back up its accusations that hundreds of UNRWA staff were operatives in Gaza terrorist groups.
The German ministries urged UNRWA to swiftly implement the report's recommendations, including strengthening its internal audit function and improving external oversight of project management.
"In support of these reforms, the German government will soon continue its cooperation with UNRWA in Gaza, as Australia, Canada, Sweden and Japan, among others, have already done," said a statement.
Mr Martin welcomed Germany's decision to resume funding to UNRWA.
He was speaking during a news conference in Jordan with his counterpart Ayman Safadi.
"I warmly welcome Germany's decision in terms of restoring and renewing and continuing aid to the Middle East and Gaza," he said.
He added that this week's Colonna report on the governance of UNRWA indicated that the agency performed an extraordinary service in a difficult set of circumstances and that it was "irreplaceable and indispensable".
The Tánaiste said Germany was a major donor to the Palestinians despite its "particular" perspective on the Middle East conflict.
He added: "I’ve never doubted Germany’s commitment to the humanitarian question."
Speaking on RTÉ's Drivetime, Mr Martin said he could not understand how "anybody would contemplate taking funding away from UNRWA, it's my personal view, given the indispensible role it has, we saw that today in Jordan in the school I went to and also in a medical clinic".
The Tánaiste described UNRWA as "key" to people's education and life progession and in future he would be calling for a "more systemic approach from the European Union and donor countries in terms of any allegations that are made".
Mr Martin said he would raise the issue with EU colleagues that in future, any sudden revelations about UNRWA or other humanitarian organisations would not meet with what he called a knee-jerk decision to freeze humanitarian funding.
Mr Safadi paid tribute to Ireland for leading efforts at EU level to get a group of countries to recognise Palestinian statehood.
He said the position of regional Arab countries was to move away from previous models of trying to negotiate a two-state solution and instead adopt a recognition of Palestinian statehood first, then work back to put the elements of that in place.
Mr Safadi said this was designed to avoid Israel having a veto over the existence of a Palestinian solution.
