Tánaiste Micheál Martin has said "up to 25" Irish citizens and dependants should be able to cross from Gaza into Egypt.
He said this would bring to 51, the number of citizens and dependents helped to leave Gaza by Irish consular services.
Earlier, Mr Martin said he hoped that all Irish citizens who are in a position to travel would be out of Gaza by Sunday.
It comes as an Irish-Palestinian man based in Co Kildare confirmed that his two young children, who could not leave Gaza yesterday due to an apparent administrative error, have now crossed from Gaza into Egypt.
Speaking to RTÉ News, Khalid El Estal said: "They are at the Egyptian side of the border with an Irish official. They are being processed there now. This is great news."
Mr El Estal's wife Ashwak, the mother of four-year-old Ali and one-year-old Sara, was killed from injuries sustained during Israel’s bombardment of Gaza.
A number of other Irish citizens and their families are in the process of crossing from Gaza into Egypt, according to the Department of Foreign Affairs.
Staff of the Irish Embassy in Cairo are at the border offering assistance.
Twenty-six Irish citizens and dependents were able to cross from Gaza into Egypt on Wednesday and yesterday and are receiving support from the Irish Embassy in Cairo.
Speaking earlier, Mr El Estal said that the past few days had been difficult.
"I didn't sleep over the last days. It was a very difficult day for me. A whole month with worrying and thinking all the time about everyone, about everything. But I need them now. That's the only thing I want."
He said his son Ali does not yet know that his mother is dead.
"I was talking yesterday morning with my child, and he doesn't know anything about what's happening. He doesn't know even that his mother was killed. They didn't tell them. I don't know how I will face him."
Another Irish-Palestinian man who escaped Gaza with his family has confirmed his 80-year-old mother also made it through the Rafah crossing.
Aymen Shaheen's mother Thoria did not make it through the Rafah crossing yesterday due to processing difficulties.
Mr Shaheen, his wife Suha and children 19-year-old Rawan and 12-year-old Ibrahim left via the Rafah crossing to Egypt on Wednesday.
Speaking to RTÉ News, Mr Shaheen confirmed his mother is now in Egypt.
"She is with the staff of the Irish Embassy at the Egyptian side" of the Rafah crossing, he said in a text message.
He said when leaving Gaza earlier this week it means he and his family, can start life all over again.
"We feel that we start our life again. We were in the grave and we just left the grave and we restart our life.
"It is the unbelievable feeling that you will start your life because we escape from such nightmare," Mr Shaneen said.
Yesterday, Mr Shaheen said he would not leave Egypt until he is reunited with his mother.
He also added he faces homelessness when he reaches Dublin because he has no place for his family to live.
He lived in Dublin up to last summer but had left his home to move to Gaza.
Just three Irish citizens were able to enter Egypt from Gaza yesterday.
Mobile phone coverage and internet access was unavailable in Gaza up until late today, having been cut off due to a fuel shortage.
The Department of Justice said that 11 applications for Irish visas from people from both Palestine and Israel have been approved in recent weeks.
It said that this figure does not include minors, and added that there are approximately eight more applications that are awaiting processing.
It said these applications will be "dealt with speedily".
A spokesperson for the Department said: "The Department is acutely aware of the grave humanitarian crisis in Gaza and is working closely with colleagues in the Department of Foreign Affairs to ensure a coordinated national response to this volatile and evolving situation.
"This includes working with the recently evacuated Irish citizens and their families who may require visa assistance."
Meanwhile in Dublin the Israeli community in Ireland held an event to mark the 9th Birthday of Emily Hand who is believed to be in Gaza after being taken hostage by Hamas on 7 October.
Cousin of Emily's father Tom, Anna Byrne, travelled from Wexford to attend the event and said that they are praying that she will be back home soon.
She said that the family is remaining positive that Emily will be brought back safe and that they "will be celebrating her birthday [with her] soon".
Additional reporting: Paul Cunningham
