The Tánaiste has said that three more Irish citizens have managed to cross from Gaza into Egypt.
Micheál Martin said it was a lower number than hoped for due to "processing delays" but he believes it is likely most will get out via the Rafah crossing by Sunday.
He told RTÉ News: "In terms of firmness, there are processing issues Rafah has proved problematic in terms of stop, start closing.
"That is three on top of the 23 yesterday, now we are very pleased with the breakthrough in that we have now 26 Irish citizens out, and we would be very hopeful tomorrow we will have more out and the day after.
"And that we will have the bulk of them out and their dependents as well within the next 72 hours."
Mr Martin held a series of engagements in Israel and the West Bank following his visit to Egypt yesterday.
Earlier, he said he had been given assurances from Israeli Foreign Minister Eli Cohen that the majority of Irish citizens still in Gaza would be able to leave within the next three days.
He was speaking after visiting two towns in southern Israel, which were attacked by Hamas last month.
He visited the Be'eri kibbutz in southern Israel this morning, where eight-year-old Israeli-Irish girl Emily Hand was abducted from by Hamas.
He toured some of the burnt out homes with Mr Cohen, as the area reverberated with the sounds of Israeli air strikes in nearby Gaza.
He told RTÉ's Six One News that listening to eyewitness accounts of what occurred in the Be'eri kibbutz, that "this was a savage, brutal attack and really inhuman in a premeditated way".
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He said he was shown photos of the mutilated dead bodies at the scene.
Mr Martin said: "One has to weigh that up in terms of the impact on Israelis and on the psychology of Israel, and I think that is important as we try and endeavour to ultimately develop a political road map.
"We must understand what is driving people and the impacts, which events have on."
Mr Martin said the loss of civilian life was appalling. He reiterated the need for an immediate humanitarian ceasefire to allow aid to enter the region and "stop the death and the destruction for so many Palestinians."
Earlier, Mr Martin thanked Mr Cohen for assisting Irish citizens to be evacuated from Gaza.
He said Mr Cohen gave him "assurances that the majority of those citizens will be able to leave Gaza within the next three days".
He added: "We know that there are some coming up today - although there has been a delay in respect to the processing side."
"It impacts on all foreign nationals coming out of Gaza," he said.
Yesterday, 23 Irish citizens, including families with children, crossed into Egypt.
Mr Martin said his impression from discussions with Israeli leaders is that there is a determination to continue with its military campaign in Gaza.
"I get the sense this morning that Israel wants to believe that it can... eliminate Hamas militarily. We don't share that view."
He said there has to be a political horizon at the end of the day in terms of how to resolve the overall situation in the region.
"I'm very clear that we we do need humanitarian ceasefire," he added.
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En route to Jerusalem after leaving the kibbutz, Mr Martin was obliged to make an emergency stop due to an air raid warning.
It is understood that he remained in his armoured car.
Other members of the diplomatic team, travelling in another vehicle, were obliged to take cover.
No one was injured and the convoy resumed its journey shortly afterwards.
He later arrived in the West Bank where he held an hour long meeting with Palestinian Authority Prime Minister Mohammad Shtayyeh in Ramallah about Ireland's call for a ceasefire in Gaza, which has left more than 12,000 civilians dead and 30,000 injured, according to the enclave's Hamas-controlled health ministry.
Mr Martin then travelled to Tel Aviv to meet Israeli President Isaac Herzog.
Earlier, Mr Herzog told the Financial Times that his country cannot leave a vacuum in Gaza and would have to maintain a "very strong force" in the coastal enclave for the near future to prevent Hamas re-emerging in the besieged territory.
Meanwhile, the Mayor of the Israeli town of Sderot, which was overrun by Hamas on 7 October, has appealed for Ireland to support his country's military campaign in Gaza.
Alon Davidi likened Hamas to the so-called Islamic State and said the Israeli Defense Forces needed to "finish the job" and not call a ceasefire.
He told Mr Martin that his 25-year-old daughter is still crying about the attack - frozen by fear when sirens sound and warn of an impending rocket attack.
In a calm tone he asked Mr Martin - are you with us?
The Tánaiste replied that applying a military solution could exacerbate the problem, warning: "Our sense is that you will radicalise the opinion of future generations even more."
He added: "We worry about innocent children in Gaza who are not part of Hamas but who are getting killed right now."
Mr Martin said: "There's a young Irish child, a dual citizen, that is a hostage - Emily Hand - in Gaza right now. The idea that small children, she has no next of kin in Gaza, the idea that small children are held hostage is just an unconscionable act."
