Some Irish citizens may be able to leave Gaza on Thursday, the Department of Foreign Affairs (DfA) has said.
Hundreds of foreign passport holders have already crossed the Rafah border into Egypt since the Israel-Gaza war started.
It is understood these would be the first Irish citizens to leave the warzone.
Tánaiste (Deputy Prime Minister) Micheál Martin is flying to Egypt on Tuesday night on a trip to the Middle East in which he will also travel to Israel and the Israeli-occupied West Bank.
A spokesperson for the DfA said it "understands that some Irish citizens may be listed for a departure from Gaza tomorrow".
"We continue to remain in contact with our citizens in Gaza as this complex situation evolves," the statement added.
On Tuesday night the Dáil (lower house of the Irish parliament) debated a Sinn Féin motion calling for Israel to be referred to the International Criminal Court (ICC) over its actions in Gaza.
The government said it would not back the motion, noting an ICC investigation into the situation in the Palestinian territories - including Gaza, the West Bank and East Jerusalem - was opened in March 2021 and will cover recent events.
Speaking for government, Sean Fleming, a minister of state at the DfA, said ministers had decided earlier on Tuesday to make a voluntary contribution of €3m (£2.6m) to the ICC.
He said that contribution is in response to the "urgent need of the court".
The government will now table a counter motion, Mr Fleming added, which "clearly expresses Ireland’s unwavering support for the vital work of the International Criminal Court".
Sinn Féin TD Chris Andrews accused the government of "double standards", saying it joined 37 other countries in referring a case against Russia to the court in 2022.
Voting on both motions is to take place on Wednesday.
Earlier on Tuesday Minister for Further and Higher Education Simon Harris told the Dáil that what Hamas did was despicable and Israel had a right to defend itself.
However he said Israel was now involved in a "war on children" and was "blinded by rage".
Meanwhile, the Irish government has pledged to do "all in its power" to secure the release of an Irish-Israeli girl who is believed to be a hostage of Hamas in Gaza.
On Tuesday President Michael D Higgins met the father and the sister of Emily Hand at Áras an Uachtaráin, his official residence.
Also present were the Israeli ambassador to Ireland and relatives of other Israeli hostages.
Taoiseach (Irish Prime Minister) Leo Varadkar met Dublin-born Tom Hand and his daughter Natali on Monday.
Emily, who is eight, was initially believed to have been killed in an assault on a kibbutz during Hamas's attack in southern Israel on 7 October.
But her family were later told she was likely to be alive and held hostage.
Speaking after the meeting, Mr Varadkar reiterated his government's call for Hamas to release all hostages immediately.
He said he would continue to raise the issue through any "avenues which may help".
"I also used the opportunity of the meeting with the Israeli ambassador to raise the issue of Irish-Palestinian dual citizens in Gaza who have asked to leave the territory," he added.
Mr Varadkar had previously said they are about 40 Irish citizens in Gaza.
Earlier in November, Mr Varadkar raised Emily's case with a number of representatives of Arab states.
Assistance for Irish citizens who want to leave Gaza was also discussed at the meetings in Paris.
Emily Hand was in Kibbutz Be'eri, about three miles from Gaza, when Hamas launched its attack.
More than 100 people were killed in the kibbutz.
They were among more than 1,400 Israelis killed by Hamas in attacks across southern Israel.
Dozens of other people from the kibbutz are still missing and it is believed some of them may have been taken to Gaza as hostages.
At the last count, the Israeli Defense Forces said 242 people were being held hostage by Hamas.
Since the Hamas attacks of 7 October, Israel has been carrying out military operations in Gaza from land, sea and air, with troops and tanks now in the territory.
Gaza's health ministry, which is run by Hamas, says more than 11,000 people have been killed in the Israeli action, more than 4.500 of whom were children.
More on Israel-Gaza war
History behind the story: The Israel-Palestinian conflict